My wife and I spent three nights in Castelrotto last May 20-23. It was a particularly late winter (by all reports, this past winter was milder), and some of the hiking trails in the Alpe di Siusi were still snow-covered and closed. There were however many trails open, and we had two absolutely wonderful days of hiking. The cable cars were not yet running from the lower parking areas, but that meant that the roads were open all day to the upper parking areas, so we were able to drive to the trail heads, and park there. There were a few shorter chair-lifts running at the upper level, but we didn't need these to start our hikes (good if you only want to walk downhill though). We got great advice from our innkeeper (we stayed at Garni Silbernagl) on what was open and where to drive to for the best trails. She also knew which "huts" (ie: mountain restaurants) were operating, so we had a destination to head to for a lunch stop on each walk.
The Alpe di Siusi is a well developed ski area, so there is no shortage of trails for walking, and there are hotels, restaurants and some small shops clustered around the top of the cable car lift, where we parked. Most of these were open last May 20. It's a beautiful area, and although not in full swing in the second half of May, I would not hesitate to go at that time.