I just returned from a trip into Tucson and had a chance to check out the snow levels on the Santa Catalina and Rincon Mountains. On the south- and west-facing slopes, the snow has melted off, mostly, to about the 6500'-7000' level and will probably continue to melt. On the north facing slopes of the Santa Rita Mountains, the snow level is lower, a bit below Josephine Saddle which is about 7000'. So, unless there is a major change in the weather, you won't have too much deep snow to deal with. That doesn't mean you won't run into icy patches of trail but I doubt that you'll be wading through waist deep fluff either.