I live in a country where it's a lot of snow right now, and I use my MB all year around. Now I have tyres with metal pegs in them so I don't fall on the ice :) If it's cold, you need to be careful with what kind of oil you use in your gears and breaks, cuz ordinary oil just freeze. I once was in this race during the winter, and it was dead cold, so everyone had to stop and pee on the gears to be able to go on for a while longer :D
Yes, definitely you can ride a mountain bike through light snow. You can actually get special winter tires for mountain bikes so they can be ridden year round.
it should! just be careful not too look like an ass if you fall :D
Shud b able to