Mt. Gunnbjörn is the highest mountain inside the Arctic circle. It is located inside glacial ice and will remain cold long after sea level locations remain above freezing year round. If Santa locates in the Northern shade, the ice is likely to remain well past the time when it has melted lower. There are several other mountains of similar, if lower, height that might suffice if you prefer the anonymity of second. Of course, most people won't climb up the cold side anyway.
Another possibility is Mt. Everest. Gunnbjörn is considerably lower than Everest. Everest's very height means that it is below freezing year round at the summit, even though it is almost within the tropics. While Everest has a certain number of climbers, they tend to follow a few paths. Santa could simply locate somewhere that is not climbable. After all, he has a flying sleigh. And of course, he's only moving in and out around Christmas. Climbers come through around May when the winds are lower. Santa could bury the entrance then.
Once global warming overcomes these places, there's always off-world. If you are not insistent on water-based snow, Pluto remains quite cold year round and will be unaffected by global warming due to atmospheric changes on Earth. Mars is a bit closer and may have water-based ice as well. Not sure about snow, I don't know that it has enough atmosphere for precipitation.
Santa also may want to consider a climate-controlled space habitat located in orbit around the Earth. Painted black with one-way glass (light can come in but not go out), his habitat can evade most notice. A little practical application of stealth technology should give it a similar radar footprint to a communications satellite or a piece of debris. By that time, there should be enough junk in orbit that Santa's workshop won't seem out of place.