Beautiful area. I worked at Philmont Scout Ranch two summers, which is just 30 miles or so NE of Truchas peak. I didn't climb Truchas thought, the peaks I did outside of Philmont were Wheeler and Little Costilla.
The earliest in the year I've been there was the last week of May and the trails were all passable by then. It was possible for north-facing washes to still have some snow on the trails, but only for a few yards. I saw patches of snow as late as July, but that was a very sheltered snow drift under some trees at almost 12000 ft.