What frustrates me is this stuff regarding, "We have no evidence one way or the other."
Nonsense. All the information we are given about regarding the Reach in the 1st PGE says that it is temperate, able to be mistaken for parts of High Rock. It's where most of the population lies, as well as the most diverse population. Think of it like the West Gash for Vvardenfell, that little slice of traditional non-crazy Imperium within the province. Aside from the Old Holds, that's where most of the cosmopolitan interaction will lie.
And with that stated, we have to ask ourselves, how far does the Reach extend?
If we look at http://www.imperial-library.info/pge/map04.gif provided alongside the 1st PGE article of Skyrim, assuming the Reach applies to the area of the map to the west and coasts where there are no mountains, that's at least 1/3 of the province that will be nice and pretty and non-snow-dusted.
If we look at http://www.imperial-library.info/maps/obcodex_skyrim.jpg and assume the same thing, that area gets potentially even bigger.
At the very minimum, there is still a big whole wedge of Skyrim that does not fit the definition of "Snow and Ice."
And that wedge exists in tandem with all the sources of cold and harsh environs. For there's no argument; Skyrim will show us snow and ice. There's little doubt about that. But it's not everywhere.