1st question: It will handle well if you have the correct tires. It is an AWD car, and those love snow. Don't be stupid though and try racing down the road in conditions like that, because then you're just asking for trouble.

2nd: Disadvantages depend on if you plan on modding the car, or keeping it stock. I've been seeing a few of those have problems with the synchros going bad and not being able to go into reverse. Aside from that, i cant remember what else.

3rd: That's debatable. Stock for stock, my car will outrun an evo x. An evo is too heavy and bulky for my liking. Full bolt ons, tune, E85, and proper supporting mods, then the car becomes a monster. But in stock form, it's fast to the average person who has never drove a car above 250hp. Let alone 300.

The Evo is a fantastic car overall. They annihilate snow and will surely provide the canyon-carving experience you'll love in the mountains. Some disadvantages are mostly with long-term reliability. Even though Mitsubishi is Japanese, I don't feel like they carry the same Japanese bulletproofness/indestructibility as other manufacturers.
If you want to spend less money whilst getting the same AWD turbo-four awesomeness, go for a Lancer Ralliart. The Ralliart is the highest trim for the Lancer, and the Evo is pretty much a different car especially when compared by price. With the Ralliart you can spend something like $6000 less off MSRP. The only real difference between the Evo and Ralliart is that the Ralliart (I think) has a marginally smaller turbo but I know it's just tuned more conservatively. You lose like 35 HP, which is hardly a big deal considering the money you save. I think it's more cost effective to slightly mod a Ralliart to get Evo-level (and beyond) performance than buy an Evo in the first place.