There is no age limit out there.
IDK about the park, but you cant ride there without a guide on a 15hp 4s sled and staying on the road anyways.
My riding bud used to take his daughter out to the mtns. She would ride with him when she was young, and rode by herself by age 12. He only buys high HP sleds and they dont stay stock anyway. Elevation kills HP.
Tog isnt high Avy danger area. Lots and lots of easy riding areas. Plenty of meadows, and plenty of flat tree'd areas to play. The trees not as tight as the UP or WI.
As long as the kid isnt a total doofus, he should be fine. Just teach him the rules before you go.
I wasn't talking about Yellowstone park, but Shoshone national forest, and grand teton national park ,which is what a lot of that area is that you ride on(CDT trail system is there too if wanted to run nice trails from tog to pinedale) and a ton of off trail all along the way!
I said what I said based on federal forest lands in my state have age restrictions and not sure there are any out there as well
I did the Yellowstone park back in the 90's before they had restrictions LOL
and really enjoyed the time in there got to see tons of critters its a nice place to visit if you never been there could be a cool way to kill a day with a kid IMO, even if you got to go slow, think speed limit is MAX of 30 mph so, not terrible, but sure not a free wheeling deal either! just saying!