The fact that virtually every RV blog has an article on how to get rid of mice, shows what a common problem this is.
Mice can quickly chew up wires, causing electrical or fire hazards. They can also chew through plumbing, and cause other major damage. Some mice carry the Hantavirus, and if you get infected you have like a 50% chance of survival.
Plug all holes and cracks. Mice hate light, so when camping, leave your hood open. String lights beneath your RV may also be helpful.
Things that may deter mice include: dryer sheets, Irish Spring soap, peppermint oil, and moth balls. An old-fashioned mouse trap can also be a wonderful deterrent.
You could also lock a cat, temporarily, in one of the outside compartments. I know, this would be cruel. So use your neighbor’s cat.
The only way mice can get into your RV, is by climbing. To gain access to your RV, mice might climb up connected hoses or cords, climb up the tires, or climb a tree with overhanging branches. Basically, anything that touches the ground and your RV, can be used by mice. Therefore, some people use tire rings, which can be made from 8 inch roof flashing. Just make a big ring and put one around each tire.
When we bought our used RV, there was at least a hundred dryer sheets stuffed everywhere, in the back half of the RV, and there were no signs of mice. The front half, however, didn’t have a single dryer sheet, and I discovered about a gallon of acorn shells inside a wall. I wonder how many times the mouse had to leave, and re-enter, to bring in a gallon of acorns. The dryer sheets didn’t keep the mouse out, they just made it build a nest in another part of the RV.