When I was at Portillo in Sept. 2007 it was blazing hot while I was there but the Inca Lake was frozen. Consequently I did a Lake Chute run each day. If the lake is not frozen you had to climb back up most of the vertical to get out. My understanding is that sometime after my 2007 visits Portillo has blasted a sketchy traverse through the lower part of the rock band so you can ski most of the Lake Chutes and get back when the lake is unfrozen.
Yes if mountain lakes are unusually deep they maintain a mostly constant year-round temperature and won't freeze. Tahoe and Crater Lake are classic examples, even though Crater Lake gets ~400 inches of snow at lake level.
Inca Lake is not as deep, but the sun is strong. It may be at 9,400 feet but it's also the latitude of San Diego.