The winter has disadvantages and advantages for both sides, militarily and among their civilian populations. Ukraine's strikes have somewhat evened out the toll on Russia's energy infrastructure, whereas in previous years Ukraine's people suffered worse.
It's not true that "Zelensky doesn't have to do a damn thing". Being on the defence against an opponent as rabid as Putin is costly in various terms, and the war's been dragging on for a long time now.
Yes, Russia's economy is really starting to show signs of severe strain. There's not enough money to pay the signing-up fees for new troops, and there's been a fuck-up in its bond market that's made an unforeseen severe dent in its already strained budgets.
Despite all that, I don't think Putin's interested in peace talks nor any form of peace that doesn't involve complete capitulation by Ukraine. He's enjoying the disarray the Trump administration's had on embarrassing display and the widespread consternation at Trump's initial supposed ultimatum and hard line against Ukraine in the recent bout of "negotiations", and the various non-military and military goading and testing campaign Russia's running in various European countries.
I don't think Putin's pushing Trump to end the war at all. There have been moves to ship in troop reinforcements to join the Russian cannonfodder - potentially thousands of Cubans have been suggested as a possibility.
If Putin has a motivation about any sort of peace talks, I think it will be more to do with discouraging Trump from imposing further sanctions (or give him an excuse for delaying them yet again). I think it's no coincidence that the Alaska talks came at a time when Trump was muttering about considering increasing sanctions somewhen.
Witkoff, Dmitriev and Vance's little stunt hasn't played out as Putin might have hoped so far - if anything, it's solidified and clarified what support Ukraine can rely on and encouraged Ukraine's non-US partners to face some bracing realities, and so far they're hanging tough. They just have to keep delivering.
It's served a purpose for Putin more as a test of how far Ukraine and its allies could be pushed along in the agenda Russia wants to pursue.
But once hostilities do end, Putin faces a very severe reckoning, as it's unlikely gains from it all will outweigh the perceived cost to his subjects, the process of converting away from a wartime economy will not be easy, and it would see the often unwelcome homecoming of troops, many of whom were severely traumatized, mentally ill, physically infirm, plain evil and pathologically violent even before their stints on the front.
I don't think Putin's in a rush to have to deal with all that.