If you do, does your insurance company know about it? NONE of the carriers that we write will cover a trampoline that does not have a net. So, if yours does not have a net around it, chances are your coverage will be null and void if they find out about it.
Is it worth the risk of not telling them? I say definitely not. It is very possible to have a claim that is completely unrelated to the trampoline, for example a fire, and if they see the trampoline when they come to do an inspection, they may not cover the fire damage at all.
Feel free to get in touch with me if you have questions about this. This is not something to ignore.