Since Santa would be foreshortened in the direction of motion, I don't think that would help him traveling down the chimney. However, since his subjective time would be slowed by the same factor, that would allow him enough subjective time to visit every household.
While be relativistic whilst traveling down a chimney would make Santa a lot "shorter" in appearance, it actually would not help with the girth. He would appear flat as a coin, which is what he would be at the fire grate.
Never mind the overpowering stench of burned reindeer from traveling at relativistic speed through full atmosphere. There would be a brief streak of color across the sky, then not much at all. Now if Santa has a warp sleigh, then all bets are off, since he is moving space and the sleight could be even "at rest" in his frame of reference.
I don't think Santa needs to go down or up chimneys, because he always came to my house, and we didn't even have a chimney or a fireplace. We had a gas burning heater in the house, largish and ungainly, but effective. Did he come down the stove pipe? Doubtful. He always stopped for cookies and milk, also.
__________________
If it ain't broke, don't fix it. Just build a better one.
Haven't you ever watched "The Santa Clause" to see how it is done when houses have no fireplace? It is pure magic. Any first grade student can tell you that.
__________________
Remember when reading my post: (-1)^½ m (2)^½
Quantum tunneling. He has a small device on his belt which increases his aggregate de Broglie wavelength until the probability of his appearing inside the house exceeds 50%, and then he waits; usually a few nanoseconds will do.
"Any sufficiently advanced technology is indistinguishable from magic."
Isn't there some sort of Heisenberg limit to that? For example, if the de Broglie wavelength uncertainty were exceptionally high, would not Santa have to have virtually zero uncertainty in his momentum?
__________________
If it ain't broke, don't fix it. Just build a better one.
My town? Come to think of it, I don't think my town has a rich part, actually; unless of course you measure wealth by the number of vehicles up on blocks in folks' front yards.
No, because we were too poor to have coal around, just butane fired heaters. Hard to put a lump of butane in a stocking, and have it stay there, so Santa must have brought that. That and a lot of those impossible Brazil nuts.
Although the Texas "GlockenSpiel" fruit cakes my grandmother used to make and bring were probably going to withstand a nuclear attack from USSR.
__________________
If it ain't broke, don't fix it. Just build a better one.