Yes, I think the size of tire, type of tire, and the weight of the vehicle are all factors. Larger tires can usually afford to run lower pressures than smaller tires. For your 80 series, if you are using a 32" or 33" tires, I would say that you could go down to 10-12 psi without an issue. BUT, what I would do is try running a little higher psi first (say, 15-17 psi), and if you find yourself bogging too much, then let some more air out. If it is a scenario where you can't even risk a bog and loss of momentum (i.e. crossing a flat at low tide) then I would go down to 12 psi, or even 10 psi if you want to take a little more chance on the bead in trade for a little more traction insurance. The reason I say to try a little higher pressure first is more for the sake of convenience. Typically if I am driving in the sand on a trip, it's only for a small segment or portion of my total trail time. I don't want to run regular dirt tracks with super low sand pressures, so if I can get by with a compromise pressure then I don't have to mess with airing up and down every time I enter and exit the sand. (Don't use this compromise pressure though if there is risk of getting stuck below the tide line, or if your engine or trans. will overheat easily).
For the trailer, I can't offer an opinion based on personal experience. My guess is that since the trailer is very light and likely on the same size tires as your 80, that you can go to the very low end of the pressure range - 10-12 psi or even lower (8 psi) with no issues. The trailer likely won't be heavy enough to damage the bead, and won't have power to the axles that could "spin" the tires on the bead.
Do a little test in your driveway right before you leave for your trip, so the vehicle has the full trip load on it. Meaure the distance from the ground to the bottom of your wheel rim at full street pressure. Then let air out until you have reduced this height measurement to 75% of what it is at street pressure. Let us know what you come up with. This will likely be the sand pressure you want to go with.