This is a tricky one and with no easy answers, weather differs from year to year and as Sweden is about 1500km (900 miles) from north to south it could be very diverse.  A "safe" period for bathing would be between mid June to mid August. (Definition: average ínland water temperature above 18°C). For skiing in the mountain areas mid december to mid April.( Natural snow offpist ).

If you travel off-season be careful; in September some "summer activities" could already be finished. For example camping areas close when August ends. Also take enough food if you're trekking on little islands because shops won't be open anymore. 

Here is a link to the latest weather forecast information from the Meteorological Office of Sweden