Congrats on the new ride! I've put over 2200 miles since Sept/16 on my Radrover ebike and taken trips to the Grand Canyon and Sedona, AZ. Trailriding can be a ton of fun (especially at night). Helmet, eye protection, suspension seatpost, and very bright lights is all your need to 4X your fun when traveling.
I'm not sure how an average law enforcement or park ranger would know if your bike is Class I/II/III, 250w-3000w, or 20-35 mph unless you tell them? I only know if an ebike has a mid-drive or hub motor and some ebikes have those components well hidden within the frame. I got into the habit of double-checking the city, state, and federal laws on ebikes if I plan to travel. Places like Sedona, AZ, don't allow any ebikes where MTB/road bikes on bike only trails because they consider them to be motor vehicles. The Grand Canyon has a little more flexibility and you can ride on the trails away from the main south rim viewing area.
I've even thought about the option of riding in ebike restricted areas without my battery inserted turning my Radrover into a +60lbs regular bike. Unfortunately, the gearing would make it hard to pedal out of 3rd gear unless I have a tailwind or going downhill.