RE: "P" tire designation vs. "LT"
I towed a fairly light trailer (4400lb loaded at the scales, + maybe another 500 lb on hitch) with my older dodge 1500 with 20inch P tires. I also had an ATV in the back. According to the numbers, I was at capacity for the truck. This worked well enough on smooth paved roads. As soon as I hit gravel, those factory GY HP's started picking up rocks (new tires, maybe 5000km on them) and leaking. I had one sidewall blow out in a small pothole. (1 trip, $600 for 2 new tires, replacing new tires)
In my case, I was at capacity of the truck. Without the ATV I'd of been fine.
What I am saying is, you can run those P rated if you aren't loading up the truck with lots of gear. My ATV is about 600lbs, with the trailer hooked up, my wife and some gear (gas cans, tools etc) I only had 1-200 lbs left on the tires and the truck payload.
I'd reccomend a tire upgrade in the future if you plan on being on gravel and dirtroads any amount... those GY HP's don't do well there loaded or not. Definitely a pavement tire.
RE: Quad and travel trailer?
You will be close to your payload limit or a touch over.
My experience doing this with a 1500 4x4 truck... its ok. Airbags are a definite recommendation. The rear will sag making hooking up equalizer bars a pain and probably stress them a bit.
Also, if you are hitting gravel or back roads to go camping, your factory (if still equipped) P rated tires may not like it. That was my curse. New tires even, and I blew the side wall out on a small bump. And picked up jagged small rock on another.... all in 1 trip. And I didn't go far on the gravel.
Just my advise.... LT tires and airbags and you'll be good to go.
RE: Air for Winterizing?
It depends... here on the BC south coast the winters are mild enough that I only blow out the fresh water lines, drain the tanks and pour rv antifreeze in the sink traps, shower trap and toilet. I use a whole jug so that some goes down the different waste pipes and gets a bit into the waste and grey tanks. I don't bother pumping the fresh line full of pink or put it in the fresh tank (which I try to drain bone dry).
If your winter temps are substantially below freezing for long periods of time, then a little pink stuff in the fresh lines and fresh tank is cheap insurance against problems. I rarely see more than a week at about close to freezing.... I know 1 year on an old trailer I only drained it all and never actually used antifreeze. If it was colder or for longer I'd go the whole pink stuff everywhere route.