I find it highly likely that before the Ukraine war is over the Poles will put troops on the ground. Historically, when The Ukraine and Belarus have not been Russian territory, then they have most likely been Polish territory. The Poles, naturally, would like to regain some of their 'lost' eastern lands. Consequently, the current conflict in Ukraine is far too good an opportunity for them to miss. Taking land requires deploying troops so expect to see the Poles on the ground in The Ukraine. Poland's recent orders of massive amounts of military equipment, including 1000 K2 tanks from Korea, indicate the line of their thinking.
Ideally, the Poles would hope to send their troops in with the consent of Ukrainians. Arriving as the saviours when the war had got to the point that Ukraine was on the verge of total defeat. Although self-interested, it would still be a brave move to stand face-to-face with the Russians, but the Poles do have an ace up their sleeve. They can offer the Russians a complete end to the war in return for dividing Ukrainian territory between them; afterall, even today, if Poland suddenly closed its border to any trans-shipment of armaments then the Ukraine War would be over. The Hungarians are already closed to arms shipments. Moldavia is blocked from shipping arms by the fact that its border with The Ukraine is controlled by the breakaway republic of Transniestria which is strongly pro-Russian, to the extent of having a Russian base on its soil. And the Romanians have only some small roads through the thick of the Carpathian mountains to use after the Russians destroyed the bridges on the lower Dniestr River. That leaves tiny Slovakia as their only significant import route and Slovakia's main opposition party is already campaigning against their involvement in the war.
And then, of course, the Poles might be able to win the backing of the USA for their move. That would constitute another huge Ace.
Apparently, the former Polish foreign minister has said that it has been discussed at high levels whether if Ukraine became a Polish 'Protectorate' it would be covered by Article 5 of the NATO constitution requiring all NATO members to come to its defense.
Of course, talk of Polish protectorates only makes sense if the Ukrainians are losing the war and badly. If Ukraine looks like being the eventual winner then look out for the Poles finding reasons to move into Belarus. Were Belarus to send troops into Ukraine the Poles might consider it enough of a justification for them to attack Belarus. The Belarussians may not be simply looking for excuses not to enter Ukraine when they tell the Russians they need their troops to guard their own borders with the West. Putin, too, might well be deliberately wanting to keep Belarus out of harm's way, in order not to give the Poles an excuse to get involved.
Indeed, the only outcome where I do not see Polish troops on the ground, is if something like the current stalemate continues, where Ukraine is still strong enough to defend itself, but the Russians are not destroyed either. If such a stalemate is quickly followed by a ceasefire agreement then the Poles might miss their chance. I use the word 'quickly' deliberately, because it seems unlikely that a stalemate could go on for many years, eventually one side or the other should gain the upper hand as they are too dis-similar in capabilities. So it seems likely that the Poles will get their chance and if the Americans and Ukrainians aren't willing to negotiate with the Russians, the Poles, I suspect will be happy to, as for them a negotiation over Ukraine will not be zero sum; but rather win: win.

The talk is that the Russians are about to launch an offensive. The question is, 'Where will it be?'
I am neither a military expert nor well-informed about the battlefield dispositions of either side, however, I am prepared to make a few predictions.
The offensive is about to happen ostensibly because the ground in The Ukraine is finally frozen hard enough to support tank movement. Therefore, one can deduce that the offensive will seek to use tanks and that the time period of the offensive, with a duration determined by the vagaries of the weather, could well be very short. That the Russians might be desiring to use their tanks to maximum effect is also suggested by the fact that we know the West has promised to send a considerable number of tanks to The Ukraine before the summer offensive season (When the ground is once again hard enough not to bog the heavy tanks) so the Russians are likely to want to attempt mobile tank warfare now before all those new tanks arrive to bolster the Ukrainian's mobile warfare capabilities. Given these preconditions we are looking for an area of the frontline where mobile tank warfare is most useful and where something meaningful can be achieved in a time period which might be as short as two weeks. By deduction this suggests that the Russians are probably going to attack on the Luhansk Front. The Donetsk Front is still in many places the same frontline as has been the border between The Donbas and Ukraine for the last six to seven years. It is deeply entrenched, heavily fortified, and frequently urban and not at all ideal for mobile tank warfare. The Zhaporizhia Front is open terrain which has fortifications and trenches only dating from May, which means they are not likely to be as comprehensive as on the Donetsk Front. The Zhaporizhia Front is a possible tank attack site, but the Luhansk Front is preferable as it too is open terrain, with a Frontline only established in September and which appears to be far less fortified and entrenched than the Zhaporizhia Front to judge by the constant reports of relatively mobile warfare that has gone on along that front since September. Additionally, on the Luhansk Front the Russians would not have to push the Ukrainians back very far to push them entirely out of Luhansk Oblast and into Kharkhiv Oblast so the politically significant claim of 'liberating' all of Luhansk Oblast would be able to be made as soon as that was done. Furthermore, just outside the borders of Luhansk Oblast flows the Oskil River, which runs from north to south in a relatively straight line (unlike the very meandering Siversky Donets River) and would make an ideal defensive line to anchor on while offensive action moved elsewhere. Given all of these factors I am predicting that 'liberating' or 'occupying' the entireity of Luhansk Oblast will be the minimum objective of the Russian's winter offensive and that if they fail to achieve even that much then their offensive would likely be deemed a failure.

Why Bhakmut and Vuhledar?
There has been much questioning in the mainstream Western media about why the Russians are trying so hard to capture Bhakmut. I would say that for the context of the war, as it is currently poised, Bhakmut is very strategically located. The Donetsk Front as I have stated above is an old frontline that is extremely heavily fortified and entrenched. Frontal assaults all along this front are likely to be extremely costly in terms of lives lost and success will only get you to the next line of fortifications. Consequently, ideally, the Russians would like to 'outflank' these fortifications and come at them from behind. Bhakmut guards the northern flank of this frontline. If they take Bhakmut they can then push South-West cutting off frontline urban strongholds like Toretsk from behind. Bhakmut also has the advantage of being on the road to the cities of Kramatorsk and Sloviansk further to the North-West, so an element of doubt is introduced about in which direction the Russians are heading from Bhakmut as Kramatorsk and Sloviansk are the largest cities remaining in Ukrainian-held Donetsk Oblast and are also significant prizes that they will need to protect. My guess is that if the Russians take Bhakmut while the ground is still hard enough to support tanks then they will swing south and try to cut off all of those frontline, fortified, urban areas while they can. They can perform the slow attritional war of street-to-street fighting in cities like Kramatorsk when the fields are muddy.
Vuhledar, similarly, is the first fortress on the way to outflanking the fortified Ukrainian frontline from the south. This is why the Russians have risked and lost so many troops trying to take this small village.

So much for the plans of sweeping tactical gains thought up while pouring over the maps in the military head quarters.
While they are hoping that these plans come off, it is likely that the Russians will employ a simpler strategy that they know they can execute. One of, while they have the men in reserve, increasing the pressure all along the frontline, and if they find a weak point, throwing everything at it in the attempt to make a break-through.