You'll be approaching Dana from the north most of the way, so you'll have the best possible chance of catching snow. The beginning of the hike takes you through meadows on the south side of Tioga Rd, just behind the Ranger hut (you really don't need to enter the park - just use the roadside parking on the north side of Tioga outside the entrance station). As I recall, there are a couple of extended slopes of maybe 30 degrees you'll need to negotiate that would be your best opportunity if the snow is deep/firm enough and not badly suncupped. As I mentioned, the wind gets pretty wicked up high along the crest, so I doubt you'll find any snow to speak of above 12K'. Your best shot of finding snowpack to work with would likely be a couple of miles or so into the hike, at around 11-11.5K'.
Once you're above 12K', the reasonably well-defined use trail kind of disappears into talus and scree. The final approach to the summit - maybe 500 vf - is pick-your-poison. Be careful on that last incline (and descent) on the talus - lotta unbalanced rock and more ankle-breakers than you might suspect.
