First things first, Jackson is COLD! ! ! I've been there and the
high for the day was -1 degree Farenheit. So be ready for that. There are warmer places to go and experience wintertime in the mountains if you so desired.
I've only been to Jackson a couple times to downhill ski, so I don't have much to recommend beyond that, it is strikingly beautiful though.
My suggestion would be that you should rent a car. Chances are high that you'll never have to drive in the snow. It is an hour and 40 minutes to get to yellowstone from the town of Jackson. Do they even run shuttles to Yellowstone in the winter?
HOw "early winter" are you planning on going? Again I'm not an expert on Jackson specifically, but for a lot of the west there are years that snow really doesn't fall until January.
THis is a cam at the bottom of the mountain today. Looks like all man-made snow. With a total of 7 trails open. I highly doubt you would be snowmobiling, cross country skiiing, etc. in yellowstone with the accumulation they've had to date.
