When hornets abandon their nests in the wintertime, where do they go, and how do they spend the winter?
Fertilised queens hibernate in a sheltered place and emerge next spring to start a new colony. The rest of them all die.
They die. Only the queen goes off to find a nice cozy spot to hibernate over winter:
An entomologist can probably tell you what kind of places they pick for their long nap.
Bumblebees and hornets are the intermediate step to show us how hive creatures like honeybees evolved.
The queen finds a nice place to hibernate - the old hollow tree or burrow under a rock sort of location. With modern houses and central heating, there are probably a lot more hiding places that are warm enough to survive, like house crawlspaces.
In the spring, the queen comes out, starts a nest and builds cells to lay a few eggs in, then forages to feed these offspring herself. The first generation is fairly stunted, since she can’t feed them as well as a large hive could. They emerge and help her with the hunting, feeding and hive-expansion for successive generations, until it’s a huge colony and the queen is basically laying eggs full-time. By the end of this sequence, she can afford to lay eggs for some fully mature adults, properly fed, to be new queens - and presumably some males to entertain neighbour queens.
Whereas honeybees have reached the point where the hive forms a churning mass centered on the queen, living off the stored honey. The workers take turns being the outside insulating layer then move in to warm up, an by spring there are enough worker bee survivors to start the hive already failry well populated.
Anywhere cool (but frost-free) and sheltered seems to work - I’ve had queen wasps and hornets overwintering in my garage or shed. I’ve also found them as dessicated corpses in my wardrobe in spring - I think the house itself is too warm and dry for them during the winter - they don’t move about in search of water or food - so in a modern heated home, they tend to dry out and die.
But of course the warm house has plenty of ancialliary, less-warm places - loft spaces and cavity walls that are probably ideal.