Obligatory big post about Krampus’ home and his relationship to it :
The entire cave is decorated lavishly: gothic architecture + interior design give it a very formal, imposing air. It is well-kempt and clean. Some of his prized ornaments and talk-pieces include an assortment of hollowed skulls repurposed as holders for red, black, and white candles, and a functioning chandelier arrayed with tealights instead of electric bulbs. The vibe is eerie, though the place is clearly beloved to him. Think of it like an underground addition to Dracula’s castle -- complete with a large study, an organ-room, and a library stuffed full of old, waterlogged books.
Inexplicably, there are a lot of teddy bears / plush children’s toys sitting in some of the chairs of his home. Krampus has a lot of empty chairs. He furnishes as if he is always expecting company; company never comes. The plushies are all worn and well-loved. Sometimes he feels like they’re the only permanent friends he has.
He’s also got a liquor cabinet and a wine-wall -- hollows in the stone that one particularly innovative goat thought the perfect size to slide a bottle through. Really old, specialty stuff. It may seem gratuitous, but remember: Krampus does nothing except make improvements. He’s hardly got anything else to do!
There are no real walls or doors, only sprawling depths of cragged rock and jaws of stalactites/mites that make up massive, semi-transparent hallways and openings just big enough for him to duck through them. When making his home, Krampus predominantly worked with the natural build of the cave’s innards, rather than carving into it. In the instance that he wants to expand his living space and does have to burrow through or physically manipulate his environment, the reno comes in slow, controlled demolitions. He does not want to ruin the base structure of the cave system; he understands how important it is to the integrity of the mountain’s infrastructure for him to keep things mostly intact.
As for him leaving his cave -- he is only active outside of the cave, of his own volition / free will, between the dates of December 5th and January 6th, with his power and motivation to do so diminishing rapidly after December 25th. Small trips outside the cave are possible on other dates, though they must be planned few and far between, and should not last any longer than half a day, nor go any further than a few miles from his home. The curse that keeps him bound to his cave outside of the Yuletide season does not seal him inside of it, there’s no Invisible Wall he cannot surpass; rather, leaving his home makes him feel weak and sickly, rendering many of his powers null. He’s simply no energy to do any harm or commit any mischief when he does so; the curse effectively castrates Krampus’ drive to Be A Menace To Society by only allowing him the span of a month in which to freely, painlessly enter society at all. What I’m saying is, if you catch Krampus outside the house in mid-June, he’s just there to, like, buy himself some grapes.
Just because he can’t leave the cave to go live elsewhere doesn’t mean he cannot use his magic to make the cave Exist Somewhere Else. If he wants to live in Paris, he’s hexing his mobile home to come with him ( another reason he’s so stingy about not messing with the cave formation too much: he’s disturbing the mountain he lives in enough just by being there, and doesn’t want any more stress to come to the site, lest it start crumbling down around him ). Krampus has to store up a lot of energy if he wants to do this, though, and will generally only move house during an absolute emergency situation.