Even if they did, based on what we're seeing in Ukraine 95% of their ICBMs would either have failed cores, failed propellant, or get lost in the Atlantic ocean.

The state of their military is really much worse than what they have been projecting. I suspect they keep their submarines in better shape so this is somewhat tongue in cheek, but even though Putin is in ways, trying to do a last stand, a Napoleonic legacy, I don't think he wants his legacy to be removing all people of Russian heritage (including himself) entirely from the gene pool. Can't absolutely rule it out, but it is exceedingly unlikely.

PS: Nuclear winter is actually a propaganda plant by the KBG in America. It doesn't exist. The world has already had more than 2,000 nuclear weapons detonated upon it, and all the nukes combined pale in comparison to natural forces like Krakatoa. That is not to imply that millions, or even hundreds of millions of people wouldn't die in a nuclear war, but anyone with knowledge of it (e.g. Russia) would have to realize that while they could make us suffer immensely, as nations and a world, we'd survive just fine, albeit missing a good chunk of population and with decades of rebuilding to do. (not underestimating the damage, just being terse).

Russia though, would not survive, as it would be on the receiving end of a much better maintained, larger, international contingent of nukes. So in truth, it's a deterrent, but it is not an offense option for Russia even if Putin is mildly crazy.