Replying to Skiing in Sweden

Yo, i'm from Chile and I'm going to sweden (Stockholm) on January until July for a college internship at KTH. I'm a huge fan of skiing and I'm wondering if it's a good idea to bring all my skiing equipment. I've been looking around for ski resorts near Stokcholm but it seems to be that the closest one is 3 hours away from there, maybe I'm wrong. I also know that Are is a pretty good ski resort but it's a 10 hour train from Stockholm. So my questions are, where is the closest ski resort from Stockholm, is it expensive, is there places to stay there (weekend travels) is it a good idea at all to bring my bag with skis?? I've never skied in Europe before and I know I will maybe regret not bringing them. Any advice from any swedish guy or people who already have been there is welcome! Peace