Hi totosparents,
If you had actual weight of the rig at each wheel, and all were below your GVWR, you could use the tire manufacturer's inflation/load charts to set the inflation to less than 80psi. But since most people don't have that information, the simpler thing is to inflate the tires to the cold inflation pressure specified on the sidewall of the tire. If you have the original tires that came on your trailer, the tag on the side should match the sidewall info.
That's the long way of saying you should inflate the tires to 80 psi when outside temps are around 70 F, you haven't towed for a few hours, and the sun is not shining directly on the tires.
One other thing. A tire that is under inflated by 20% is considered by tire manufacturers to have been "run flat", which may have caused permanent internal damage to the fibers. The damage can show up unexpectedly in the future. Goodyear suggests having their tires inspected by a Goodyear professional if they have been run 20% under inflated.
60 psi would be more than 20% under inflated. If your trailer was loaded very lightly, with no water, you might be ok. If you were loaded heavy, you might have a problem.