Very few parks in the area. The horse park is essentially on campus and there is a new road that connects it to the stadium. You might try the following places, but you'll be anywhere from 20-40 minutes away without gameday traffic, so you'll need to account for that. MDOT just added median barriers for the entire stretch of MS12 through town, so gameday traffic can be an epic pain.
No idea if any have space or hookups:
KOA at Oktibbeha County Lake
Indian Mound east of Starkville off of US82
Choctaw Lake in Ackerman
Jeff Busby Campground on Natchez Trace
Lake Lowndes State Park in Columbus
Lake Tiak O Khata in Louisville