Trees notwithstanding, you do NOT want to be the tallest ground rod in the area, nor do you want sharp pointie metal things in the air; there is a reason that lightening rods on buildings and towers look like that. YES, disconnect the power, and get the cord up off the ground, because if you don't and are unlucky enough to get hit, that cord just laying on the ground will arc through and probably take anything plugged into the RV out.
As for tires being a good insulator, I would agree as long as the jacks are pulled up. Good in a driving rain? Absolutely not... There was a news truck several years ago here in LA that parked up off of a sidewalk with one side of it next to some grass with the sprinklers that were on at the time. The operator raised the mast into what I think were ~16kv power lines.. That energy went through the fiberglass dish (about the same size as a Slimline), found the copper mesh, down the telescopic mast and welded the sections together in-place, through the truck, 200' away via coax from the truck to the camera, blew the camera apart as it found ground through the tripod, blew the operator away from the camera and injured her badly. Back to the truck where Adrian Alpert was sitting inside.. because the tires were now completely washed down, the energy went straight through them, and cauterized the rubber from the wheel to the ground... IE- wet rubber = conductor at these levels. Ardian would have been fine had she stayer inside. Instead she opened the door and stepped out while her hand was still on the handle. At the end of the day Adrian lost most of one arm, pieces of legs, and I don't remember what else. It can be Goggled, but the lawyers squashed a lot of the information.
At the end of the day it doesn't matter what kind of insulator it is because lightening doesn't care. If you are in a car or RV, stay there and away from metal (and pull down the "come get me's"). The trick is that you want your body to rise at the same rate and potential as everything around you, even if it's a million volts, that's OK. What you don't want is your body or the cage around you to rise or fall at a different rate. That will probably ruin someones day.