This issue has come up several times before. There are two problems, one that not all provinces have the right climate value, the other that there is a bug in winter appearing and working properly.
The first one is easy to fix, it just needs people dedicated enough to research the changes required. I'd be pleased if someone ran a thread in the Bug Reports forum to get this cleaned up once and for all.
FYI, The values for Climate in provinces.csv are, as best as we know:
0 - Snow, October through May. It is most prevalant in November through April.
1 - Seems to be desert type weather.
2 - Certainly no snow with this value. It appears in a couple of Baltic Sea provinces, a couple of South American provinces, most of North America, and one Siberian province. it might be intended to provide very occasional snow, but still, the province assortment is wierd.
3 - No snow.
4 - Tropical climate.
5 - Some snow December through February.
6 - Tropical climate. This one seems mostly used in equatorial provinces, compared to a value of 4.
7 - Snow, November through March. It is most prevalent in December through February.
8 - Snow, June through August. Used in the southern hemisphere and in a couple of Afghani and Indian provinces (north of the equator).
The bug I don't hold much hope will be fixed, I'm afraid.