Hi, Eric,
Take a look at
this post from last Saturday. Here's one example:
This isn't by the tram, but just across Banning Pass from the tram area. The snow you see is about what you should expect at the top of the tram. Normally temperatures are 20 to 30 degrees cooler at the top of the tram than they are in Palm Springs.
Up to you, but personally, I wouldn't head up there with hiking shoes. This time of year, I wear heavier full-leather hiking boots with snow gaiters. Also, a light jacket might be OK, just OK, if everything goes according to plan. Dunno about you, but I've had my hike plans go south on me more than once. Having something a bit heavier might be in order.
Re walking down from the tram, that's a steep, precipitous route. Note the use of the word "route," not the word "trail." This time of the year with the snow and such, it's more mountaineering than hiking. People have slipped and fallen to their deaths on that route. If you're a competent mountaineer with technical equipment, go for it, but that's not what I read when I hear "light jacket" and "hiking shoes."
Just FYI type stuff,
HJ