the reason the war will end in mutual exhaustion is basically this.

The Russians cannot shift the military front as they no longer have enough functional combat power to do more than man heavily entrenched defensive positions. The Ukrainians are now in a somewhat similar position unless the greater West starts delivering serious MBTs to them which so far has not been done. The Ukrainians probably have better artillery and short range strike weapons now overall, but the Russians have some functional air superiority and still maintain some long range fires capability and despite rapidly improving Ukrainians AAA and mid range SAM capabilities, no defense is 100% and the Russian while taking air attrition can keep it up for what I see as the remaining length of the war (90 or so days)

So the Russians are striking what they can (stationary large civilian targets like power plants) and the Ukrainians are hitting what they can (picking off Russian tanks/IFVs and battlefield level artillery positions as the entrenched areas offer up stationary targets).

The Russian tactics now will not end the war. The Refugee issues will be spread over the EU + North American etc and do not represent a strategic threat. Also as the Ukrainians are European culturally, this is very unlike the Syrian refugee crisis which the EU survived. Further causing this civilian crisis in winter is going to feed directly into the Western picture of the Russians and further generate popular support to continue to give weapons to Ukraine. The RUssians have mis-played this war in a publicity sense so badly that were their enemies to place spies into the positions of power in Russia to control their actions, its basically impossible to think what the enemy spies could do differently to make the images worse. This will be studied as one of the greatest modern failures in warfare for any nation in broad spectrum of ways (PR, battlefield preparation, equipment failure, strategy, field level tactics, etc) ever.

Nonetheless, since the RUssians cannot affect the Ukrainian military supplies effectively (they can bring in enough material from unbombable border states to maintain combat power) and the Ukrainians can similarly not bomb Russian strategic level supply depots, there is now very little that can change on a battlefield level without some sudden change in the combatant's macro conditions (the US suddenly withdraws support or Putin is deposed kind of stuff).

Expect negotiations to seriously start sometime in February or March, after the Ukranians spend something like 60 or 90 days probing the Russian's defensive lines to see if they can find some miracle weak spot (I guess it could happen but its extremely unlikely now) and don't make any significant progress and the Russians continue to expend troops and increasingly precious equipment for nothing tangible and the general lack of supplies and parts for many Russian systems continue to degrade functional combat power for offensives.

The final lines will be the eastern parts of the LNR/DNR republics put into Russia formally and more importantly to Russia the the line from Dontesk to the River will likely be held in the South and that part of Ukraine incorporated into Russia as well, giving Russia access to water for Crimea as well as a full "land bridge" to that area, plus the Mariupol port which is of some use and total control over the warm sea of Azov which is a strategic russian shiny object they've always chased.

As a side note, due to economics and declining population, Russian land warfare combat power will not recover to previous capacities during the lifetime of anyone reading this message unless your in middle school. They've destroyed it completely as almost all of its power was based on Soviet stockpiles and older gear being rebuilt and modified, nearly all of which now has been consumed or lost and nobody will replace it.