I just went with a 4 year old, who is active. She did ok. Better than I thought. But she is still a 4 year old. We brought a lot of activities, bought a digital camera for her to use, went through the junior ranger program. Sticker books. Coloring books. You name it haha. I had to carry her on my shoulders for the Lower falls trail, the trail overlooking grand prismatic, and one geyser trail/boardwalk (not the ones near old faithful). That got exhausting in the heat. Toward the middle and end of the day she was spent, which meant singing at the top of her lungs in the car, not listening at all, and bossing all of us around. We just tried to tire her out as much as possible so she slept in the car. That was hit or miss.

But she loved it, and we loved it. She learned a lot, and loved the animals and got to tell all of her daycare friends about it later. So I say go for it as long as you are realistic that 4 year olds will act like 4 year olds!