I did this as a 3 day, 2 night backpacking trip. I would beware of snow still covering the trail as we had lost the trail several times and ended up following the cascading stream that originates at Horseshoe lake. There seemed to be someone's bushwacked trail that was very steep to climb with backpacks(even came across a well made campsite along the way). So, if you do lose the trail, you could always follow the stream all the way up to the lake.
Snow was also covering parts of the trail in the last mile up to Wheeler peak so I opted to climb straight up and around the snow. I'm not a fan of walking off the trail but I have no experience walking on snow and the few times I did I nearly slipped off the mountain!
Thunderstorms seem to roll in consistently around 3-4PM and last a few hours. We were back in the treeline by then. Pea sized hail will fall during the storm, so make sure you have something to cover your head (my baseball cap did the job just fine).