The free TV here in the USA is not satellite based - strictly line of sight. It works well, I've gotten HD broadcasts as far as 50 miles away from larger cities - over flat ground. I would be a little surprised if you could get it inside Yellowstone, but I have not tried.
If you really want dependable TV, then I would suggest the Dish Pay as you go. I've been using it for 3 years as a fulltimer all over the USA, including Wyoming, Idaho, Montana, and Colorado, also with the Winegard Pathway X2 and their dedicated tripod stand. I like these portable units because you can move them around trees, poles, etc to get a good view of the satellites.
The X2 bundle which includes one receiver box (decoder box) and one remote control is currently $450 on Amazon with free shipping. Camping World also carries them and can have a good sale price. The X2 can get either the Dish eastern or western satellites so you have twice as many choices in case one set is blocked.
Note that as you go further north, it is tougher for the receiver dishes to see the satellites over the trees, mountains, etc. because the satellites are sitting above the equator. Yes, you also need a decoder box and a subscription plan. Dish has several plan choices.
Many (Most ?) of the satellite dishes will get Dish or DirecTV only - not either or both. You will need to check your current setup to see which one it's set up for. Bill.Satellite is the expert on this and I would suggest sending him a private message if you need help determining this.