Marrakech gives a very European impression of Morocco. Head just few hours out of the city and you'll find a completely different atmosphere.
Modernity isn't a big thing in the mountains south of Marrakech, where Berber culture is strong, and tourism mainly confined to trekkers. Two specific draws are the snaking road south to Taroudannt; and Imlil, Asni and Aremd, the Berber villages en route to the highest peak, the Djebel Toubkal. But sights aren't what the High Atlas is about – it's the views. Almond blossom at Ouirgane; winter snow at Ouïkaimeden; wild nature and traditional villages all year round.
There's skiing of a kind in Oukaïmeden in winter, though good snow isn't guaranteed. Trekking is best in spring when the almond blossom is particularly lovely. The cooler temperatures in autumn make this a good time too. High summer is still a good time for the mountains, unless you're intending to climb Mount Toubkal.