Not sure yet about Yellowstone. It's not part of the photo trip but I may fly in a few days earlier and go on my own - being alone would definitely limit where I am willing to go off road/path but it would give me a taste of it and since it is a very long flight for me I may as well take advantage of it. I might see if anyone else on the tour is interested in meeting a few days early to share a rental and spend a day or two there.
Although I've been through the Tetons, it was many years ago, so will not talk about that.
Yellowstone is worth a try, even in the winter. As I wrote above; get the app that informs of road closings.
Coming in the South gate, Old Faithful Geyser Basin is a fairly short drive, and is worth a stop. For one thing, there are other notable geysers nearby that you can walk to. Plenty to look at. Additionally, that is one of only two places in the park to find food in the winter. If you can call it that. After our first experience with the grill menu, we took sandwich makings the next time and made sandwiches in the parking lot.
The upper falls and the grand canyon are a relatively short drive from there. Everything takes time to get to, and the speed limit is 45 (and sometimes lower). There will be ice and snow in patches, so be careful. If you are unsure of driving a rental car in the park, see if you can book on a tour bus.
On my trip, I was primarily taking snapshots of the family at the places where we walked. I was hoping to catch a shot of bison with geysers, and I did get some, but nothing like setting up a shot with a tripod, etc. If you have a gadget bag that will hold camera, several lenses, and a short tripod, do that. I don't know what arrangements the photo tour has for the Tetons, but going on a tour bus might mean carrying only one bag.
I have about 500 shots to go through, and haven't started yet.