Travelling by air is fast and easy.
Fly to Stockholm and then on to Åre (Åre Östersund Airport) with SAS or BRA or fly with Jonair from Stockholm to Härjedalen Sveg Airport. During the winter, you can easily get between the airports and Vemdalen by airport transfer. From Åre Östersund Airport the distance to Vemdalen is about 120 km and and from Härjedalen Sveg Airport the distance is about 70 km.
You can also fly to Værnes, take a transfer to Åre and then bus and train to Vemdalen.