It really depends. I mean it is a long country so the weather at one end can be totally different to the other . I think where I live , in the middle/ the southern north…! , the best time is vårvinter (spring winter) like march april time. Longer days , loads of snow and often sunny. Skating on huge lakes , snowboarding , cross country skiing etc. July can be fantastic , basically light all day , beautiful air and nature , same as september for autumn/ hunting season ,
I wouldnt visit prob december/ janauary as the days are very short and it can be bitterly cold (-30c last year) I love it all year but thinking from a guests perspective. Do you want city stuff? Culture ? Or outdoors/ mountains etc …? Where i am , October is a bit of an inbetween month . MTB is winding down as the days are getting shorter and the snow is coming, but there isn’t usually enough snow for winter sports. Northern lights are go though and the hunting is on so can be great for camping!
Edit : yes I’m in Östersund , 1hr from Åre