I live in Spokane currently and went to college here. I'm moving to Minneapolis since I want to be in a bigger city with a larger single-young-professional population, but Spokane is pretty great.
Snow - don't worry about it. The last time people were seriously snowed in was in 2008. The weather isn't as mild as the west side of the state (grew up in Seattle), but it's drier and sunnier.
Crime - Spokane is fairly high for property crime, lower for violent crime. It is, of course, dependent on the neighborhood. I'd agree with everyone else that you should stick with the south hill. It's not ideal for biking, but lots of cute houses and nice neighborhoods.
One of my issues with Spokane is that people here tend to marry young and stay very family-oriented. That makes it difficult to build a social circle if you're a single adult. Even at 25, the majority of my friends are married couples and dating is very difficult. If you're moving on your own, I'd be aware of that. However, the outdoorsy community here is super active. I'd recommend Spokane Mountaineers if you're at all interested in that sort of thing, people seem to make great friends there.
Spokane is really beautiful and has everything you could need - a small downtown, all the chain stores you're used to, plenty of coffee shops, restaurants, breweries, and affordable housing (which is why I didn't and won't move back to Seattle). It's still pretty small, you'll never drive more than 15 minutes to get somewhere. The pace of life is fairly easy - you won't have a painful commute, parking downtown is fine, COL is low. I'd describe Spokane as a very comfortable place to live, moving to excellent if you are big into camping/hiking/rock climbing.
My complaint comes down to the fact that the city isn't big enough to make room for the "niche" things you might get involved in somewhere else. For example, I love swing dancing. In most big cities, you can go dance with a whole community of people 3-4 nights a week, easily. Here, it's kind of a dinky dance once a month.
In summary, it's a lovely town and I'll be sad to leave. Hope it's right for you!