I'm looking for recommendations for climbs, treks, via ferratas or mountain biking (especially single track) in the Dolomites for the 4-15th June. We are a group of 4 Kiwis (New Zealanders) with a lot of mountaineering experience (one is a mountain guide). We are quite keen to visit the Brenta group and do a hut to hut trek/via ferrata, but it seems we're a little early and most of the alpine huts and lodges are still "shut" over that time. Is it possible to stay in a "winter room" at the same huts, or is everything completely shut? We don't mind being self-sufficient and having to deal with tougher conditions, as we are used to long days, very basic accommodation, carrying heavy packs with our own food and overnight gear (cooker, pots, sleeping bag, mat, etc.) from mountaineering trips in NZ. We're particularly interested in the more technical treks or climbs.
Any recommendations for suitable trips over the period 4-15th June would be very welcome (as well as suggestions for cheap accommodation)!