I have the similar truck, well 06 tundra but not step side.
I have a 3500 lb trailer 6-1/2' wide, 10 feet long 26" sides. Which filled level will "physically" hold a cord. But it starts to fishtail when towing over 45 mph.
Loaded with birch (green) about 5,000 lbs/cord.
I just hauled 1.5 cords in 1 trip from a highway project. (trailer a little over full on the front (tongue weight heavy to help not fishtail)
Split, stacked & measured (198 cubic feet) the last load (which was a little lighter than previous loads )
The truck will hold just over 1/3 cord if I load it just a little above the sides. (but the head lights point to the moon)
The trailer had over a cord, I was over loaded a little so I drove 40-45 all the way. Spring almost bottomed out on the trailer & was real careful on bumps & heaves.
All this is to say, your snowmachine trailer will haul 1,000 lbs max, your truck will haul what you can safely fit in the bed.
so if you take some straps, & drive slow 3/4 cords or just a bit less would be a pretty good load.
PS Inflate the truck tires to the max (45-50 psi) before loading that much weight, I was lucky & had a battery air compressor to fill the tires, they looked
almost flat. & take a piece of plywood to put in the bed to cover the rear window glass & load the cab end of the bed heavier, ahead of the rear axle (some weight will be on the front tires that way)
When I stack it above the bed, I strap the front 2 rows down too (or any rows that need it). Don't want any rolling off or hitting the rear glass.
top right shows how much a PU various sizes will haul: (broken link removed to http://forestry.alaska.gov/pdfs/08BTUFirewoodHandout.pdf)