There is an Icon store behind City Hall... It's indoor service where there is no snow.
Ms. Liberty, Back Alley Brawler, and other trainers in the game letting you change out your costume is a convenience. I know it's not perfect that the snow shows up in the creator screen with them, but I don't really have an issue with it when they are bonus tailors and there's another perfectly suited option in the same zone.
Even still, my desire for snow remaining would be limited to just the snow on the ground sticking around for an additional month. Let the skies clear up, but don't have the fallen snow (and frozen water) melt away so quickly as soon as January hits.
Also, I'm pretty sure this isn't an addition just this year. This was here last year, as well as in game on Live before the game went away on us those many years ago.