I think it makes more sense to break this question down into a few specific ones:
1. How likely is it that Putin will want to use nuclear weapons?
- I don't think he is that mad, but who knows? If the pressure inside Russia starts to rise, protests expand and a win in Ukraine starts to get more and more unlikely.. Cornered animals start to lash out. If he thinks it's his last chance to save himself or his legacy, he may go that far. Do I think he would attack a NATO country? No. But maybe he would attack Ukraine and hope that would somehow save him.
2. How likely is it, that his orders will be followed?
- He seems to have surrounded himself with yes-man, so I don't think some higher up would stop him. But just like with Stanislav Petrov it's often people down the line who, when faced with the actual consequences of their actions, choose to do the right thing.
3. How likely is it, that they will hit/explode?
- I have no sources, and it's just a personal feeling: I think the U.S. and probably even China have technologies to shoot down any Russian nuclear missile attacks. Looking at some UFO videos, which have popped up, and my belief that those aren't alien but advanced military aircraft, I think this would be a good bet to make.
Whether they would use it to save Ukraine and show their (technological) hand is another question. But I would say the chance of a Russian nuclear missile hitting a NATO country and exploding is pretty low.
4. How likely is it, that it will trigger a response?
- If it explodes in Ukraine, who knows. The war in Ukraine would be over at that point, I think it would more likely trigger an (extreme) non-nuclear response, which would result in Russia being made unable to further attack and Putin and his inner-circle being obliterated. If they attack a NATO country, all bets are off.