“Yes, your insurer may cancel your policy if a trampoline isn’t in their underwriting guidelines or they don’t want to extend insurance to those who own trampolines.
You should get plenty of advance notice if they cancel your policy, but keep in mind that an insurance company finding out you have a trampoline is also highly unlikely.
However, it’s better to be honest with them. If you’re concerned about it, call your insurance or look up your policy exclusions. Your terms and conditions should list any exclusions or reasons why your policy may be cancelled.