The A-1 lake campground has been closed for years. Reservation permits are required for all activities on tribal lands. A close look at the tribal regulations might keep you out of trouble.
You completely should like the Mogollon Rim Mountains. While you're here at Sunrise Lake and you want to go for a horse ride, you may go to Wiltbank Trail Rides. The summit of Big Cienega Mountain can be made out from Sunrise Lake; you can stay the night at Sheep Cienega
Campground. Everyone likes Sunrise Park and its 800 acres of skiing land. 80% of the trails are easy while 20% of them are hard and well suited for proficient skiers.