The best months are June, September, and October. In June, the high meadows are still green from snowmelt, the daylight is long, and the summer crowds have not yet arrived. September offers cooler temperatures, stable weather, and the start of autumn colour in the beech forests. October is splendid for colour but the weather becomes more unreliable.
July and August are peak season: the Cares Gorge is genuinely overcrowded, parking at the Lagos de Covadonga is impossible without a shuttle, and the main villages fill up with Spanish holidaymakers from the hot interior. If you go in August, start early and head for the less-visited eastern massif. May is cold at altitude with possible snow on the high routes, but spectacular for wildflowers. Winter closes the Fuente Dé cable car on windy days and makes many high routes inaccessible, but the park is quiet and the lower valleys retain their charm. The mountains receive significant rainfall year-round — this is not the dry Spanish interior but the Atlantic north, where green means wet.