Hey Chad...delayed answer, and probably not what you want to hear, but..."it depends". Really. As you allude to, it is more a question of weather and snow than it is a date on a calendar. As you probably know, sometimes you can be at 10,000' feet in 2 feet of snow in mid-October, and sometimes you can be there mid-November and hardly have any.
I've taken my kids first season to hope they don't freeze, and it is bitter cold and snowy, only to go almost a month later with my own tag and sit around camp at 10,000 feet shirtless catching some rays and napping. Impossible to predict.
Question is slightly confusing since you mention 3rd season and then also mention rut in mid-late November. 3rd season happens usually late Oct/early Nov, well before the rut typically (on purpose I suppose to avoid having rifle hunters hunting in the rut).
Nevertheless, unless the high country is just hammered with deep snow, many of the deer will stick around up high. They won't be in the deep snow on N. slopes, but many S or E facing slopes will melt off with a few good sunny days and deer will stick around. My experience is most tend to hang out lower overall (quantity-wise) than elk, but there are still some nice ones up high. The bigger factor will probably be rifle season pressure, vs. archery pressure - there tend to me many more hunters in the woods, and rifles going off which will move them elsewhere more than a few snow storms.
Best bet is to have 3-4 good options that vary in elevation and distance from the road. Try your favorite spot, and if some snow shows no tracks, you can move on to plan B and not waste your time. Sorry...it just depends...won't know until you try it, and if it's great this year, it may not be great next year depending on weather etc. Gotta be flexible usually and have Plan A, B, C, D etc. Good luck.
