Yes, but the Biden Administration has repeatedly stressed that a an actual confirmed (limited) tactical nuclear attack by Russia on Ukraine would NOT trigger a US nuclear response, but instead we would make a devastating response by conventional means. I assume that means taking out vulnerable Russian military assets, but of course simply wiping all Russia’s refineries would potentially be on the table, for one example. So much of the Black Sea Fleet is out of commission that I don’t know if removing the rest of it (fairly easily accomplished) would be considered sufficient response.
You forget the fleet of Russian nuclear missile submarines patrolling the Pacific, Gulf and Atlantic coasts.
Nobody wins a nuclear war.
Every war game says once the first nuke goes off every nuclear power on Earth launches theirs.