Replying to Snowbird/Brighton camping trip

The semester is almost over but I'm hoping to get one more week of skiing in after. The plan is to drive from Colorado to Utah on May 9 and ski the 10-14th. My dad is going to come in the middle of the trip and ski two days as well so I will have a hotel for a couple nights.

Where can I camp within 30-45 minutes of the resorts? I have a camping setup in the back of my F-150 that I will be staying in for 3-4 nights. I am not looking for campgrounds so is there any dispersed camping/BLM land in the area that allows camping? Preferably somewhere more in the wilderness and not too high in elevation so that it is not too cold but I am flexible.

Does snowbird have any groomers that late into the season? My dad isn't the strongest skier anymore so I need to go somewhere for a couple days with options for him.

Also, is it worth doing a day at solitude?