Unfortunately there aren't many options for non-glacier skiing around Trondheim in august. The snow that is left is melting fast these days.. Alnestind in Romsdalen/Trollstigen could still be an option, however that's a 3-4 hours drive from Trondheim. I'm not sure how the western parts of Jotunheimen and Strynefjell are doing snow-wise, and most potential ski-trips will involve atleast some glaciated terrain i think.
When studies begin you should get in touch with Ski-/fjellsportgruppa and/or Tindegruppa at NTNUI, for meeting students with similar interests. It's also possible to borrow/rent glacier equipment.