Not so much Åre village itself, but the surrounding villages of Vålådalen, Storlien and others have great fell walking trails. You can walk for just a few kilometres up a fell or for days between fell cabins with your own tent. The choice is yours. A comment from me as a parent: children usually love this as they are completely free to roam and love adventures.
Equipment: Equipment depends on how long you will stay and walk but sensible shoes are a must as is mosquito repellant in July-August (although autumn is a nicer time with glowing yellow fellsides - in spring it is usually too wet after snow melting). A small first aid and emergency repair kit, a tent if you won't stay in fell cabins or stations (in stations they often sell dry and tinned food)...
Let's face it. Skiing is what people come for in winter and there are around 50 lifts in the area, the cable car up Åreskutan and also cross country trails galore if that's your preferred way of skiing. World Cup slalom is often held here and 2007 will see the World Championships. You can stay in Åre itself with easy access to the cable car, or in the many areas around it, such as Duved village to the west, or child the child friendly Björnen complex.
Equipment: Åre village is full of ski service and rental places.
?re Ridcenter (signposted from E14) and several others offer treks up the fells on reliable Icelandic horses. The best thing is that you often see animals closer on horseback since they can smell the horse but not you...If you want a true adventure with treks across great mountains and sometimes nights in Same tents, then go for one of the various treks with environmentally certified Vemdalens Islandsh?star. They start from STF Storulv?n fell station and treks vary from 2-5 days as do the experience needed to participate.
Why not have a go with dogs yourself. Perhaps in the hands of the Swedish Champion Tommy Bernhardsson. Our daughter is too young but one day I hope to try and "fly" with the dogs. Tommy does anything from half days to weeks and can include other activities.
Paragliding is a popular thing in summer. At the cable car station on Åreskutan is a cabin for the gliders who throw themselves out and circle above the village and then down to the "Draklanda" landing place by the lake. You see them from early in the morning on a clear day - some find thermal currents, some not.
That's what the week in July is called when serious cross country bikers gather here to get up the Åreskutan and bike down! I call it crazy but there you go ;-) It is also possible to bike the rest of the summer and when bikers aren't on Åreskutan, they can be found in the small "training area" next to Åre Skidby or all geared and hyped up in one of the bars :-)
Equipment: The tourist office in Åre can tell you the current places for renting bike and equipment as you need a well equipped bike to go down a mountain...