It would likely be your insurance for both. It is then your carrier’s job to subrogate your damages from any at fault third-party. It would likely be seen as an “act of god”, unless you can prove the campground had knowledge that the tree was dead, compromised structurally making it as risk to fall and failed to take action. As a camper, you are a “Business Invitee” which raises the duty/expectations of the campground management to ensure a safe environment. Good news is that this type of loss should not impact your premium.