I think it mainly depends on how low the snow goes. If it is below 8500 feet , there is the potential of getting lost and misdirected. Have you done it before? It can become very confusing in the traverses below 8500 if they are covered with fresh snow, and there is only one (safe) chute up. The other variability is your comfort level with winter mountaineering--i.e. do you have/have you used crampons or yaktrax, an ice axe, etc? Some of the slopes below 8500 are very steep and have exposure. When the portion from 7000 to 8500 is covered with snow or ice, people have fallen and even been killed there. If going up steep snowy slopes is something you do frequently and you have GPS (or have done it before) and you are (very) well conditioned, you should be okay. Also, it seems likely that it will stay warm enough that the snow dump below 8500 feet will be very trivial or non-existent. Rain will make the trail muddy obviously but not to the point of obliterating it. As far as the part from the tram to the peak, that's actually less concerning,( so long as you have proper gear), because it is less steep and there's signage and more people around.
If you have never done any winter mountaineering and the latest weather reports indicate significant snow below 8500, then I would say no, don't go. If there is no snow below 8500 you should be okay. That's my two cents.

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