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I'm very new to the RV world and plan on leaving from Montana to Florida in March. Because I'm self contained I plan on cold camping for the entire trip at rest stops, truck stops etc. My question is, is this a safe thing to do or am I taking a chance. Also I've never towed my 36' this far, so it's like I'm entering the unknown. Any suggestions?
Overnighting at rest stops is often illegal -- you have to check the laws for the applicable state. You could surely get away with stopping and sleeping for a couple of hours at a time. Two hours is enough time to make you fit to get back on the road. I would also have to point out that plenty of people get away with overnighting at rest stops -- even when it is illegal. I recall that in October of 2002, "DC Snipers" John Allen Muhammad and Lee Boyd Malvo successfully overnighted in plain sight at an I-70 rest stop near Frederick, Maryland for nearly three weeks while they were the object of one of the biggest man hunts of all time. So... Yeah, I don't think you'll be noticed while sleeping at rest stops. Just kick back and don't worry about a thing.
Truckers generally don't appreciate RVers and treat them as a nuisance. That doesn't mean that they wouldn't come to your aid if someone started beating up on you, though {shrug}. If you pull into one of "their" lanes, however, they _might_ be so bold as to suggest that you "move that hunk of junk on down the road".
I was a tent camper all over the (civilized) world for decades. Not once did anyone ever so much as bother me or any of my possessions (although I've met people who have suffered same and who have had relatives killed while camping). It wasn't until we got an RV a couple of years ago that I started packing "heat". Mostly, it was the other RVers that scared me {grin!}. When I realized they were all armed to the teeth, I felt I had to escalate {grin!}. Realistically, I have never assembled and loaded the weapon while we were camped for the night (not _yet_, anyway) but the day might well come when I pull it out and whack some other RVer over the head with it {grin!}.
By far the _biggest_ risk that _you_ will be facing is the act of putting the key in the vehicle's ingition and turning it. The American highways are deadly. I helped scoop 14 dead and injured vacationers off the side of the highway in 2006. All other vacation borne causes of death: getting hit by lightening; venomous snake bite; bad food; sceptecemia from splinters; carbon monoxide poisoning; etc. -- pales in comparison.
So putting everything in perspective, be careful out there on the highway and you will probably cheat death for another day.