I personally would not take one tent camping. There is too much risk of a wild animal smelling her and getting into the tent when you are not there. Of course, depending on the campsite, she could stay in the car while you aren't around but that would only be if the site is very shady with no risk of sun being on the car.
We used to take my daughters bunny camping and he loved it. We have a small house trailer so there was no worries about leaving him in the trailer while we were at the beach or hiking. The animal must be in a 100% escape proof cage and the cage must also be mosquito and bug proof. We used a baby stroller bug net to cover Bun's cage with. He absolutely loved going camping and we had a table that his cage sat on and he would sit with us whenever we were sitting outside. He had a special cage just for camping.
For a hedgehog, heating is an issue and a snuggle safe wouldn't be much good unless you are at an electrical site and take a microwave. You could stock up on mitten warmers but if it got very cool at night they would not work very well. At night, you could keep her in the car which would stay warmer and wrap the cage with blankets to hold more heat in.