I farm for a living, I have a farm with hills, and moving hayracks of hay & wagons of grain up & down hills is my game. I also do firewood. I even have a 1720 tractor with loader, slightly smaller than yours. So maybe I can help some.
One of the scaredest times I ever had was on that tractor when I went down a hill with an empty grain wagon, about 2000lbs. The weight pushing makes the rear end real light; the loader makes the rear end real light; I about lost it & wrecked bad, & I'd been driving tractors & wagons for 3 decades.....
I called the coop the next day & had the rear tires filled (3/4 full) with calcium cloride. I don't know how they ever sell a compact tractor with a loader on it without filling the wheels. The most dangerous thing I ever been on. Only had it 1 week without fluid, and what an aweful thing, most dangerous I've been around in my years of farming. (And I've used a buzz saw with dad; and have one of those Unicorn style wood splitters, and our main loader tractor was a narrow front which dad had 500-1000lbs on the back - all much safer than that unbalanced tractor!
Now, with a wagon on, you can't be hanging anything on the 3pt. So, if you want to do this, you _need_ to have the tires filled, or steel weights on it. Serious weight.
That made this tractor very useable for going up & down hills. (Well, my favorite tractor - gets used every day - I put a weight box on the back with 500# of rocks for serious work, but the fluid made it useable without.) This is my preaching for the day. Have weight on the rear wheels or you will die.
The wagon will work well. I would look for one with the deck rotten off of it. Throw all the wood deck away, & just put the logs on the frame of the wagon. The front & rear axle are built up to be the frame, and there are little cogs up in each corner to hold the deck beams - exactly the framework you need. Nothing more to build up or add. And a rotten top will make the wagon pretty cheap. All you need is the running gear.
I think your tractor will find 3 ton a good load going down a hill. My opinion. I'd start small, work your way up to what is comfortable. Green wood is _heavy_, you will get to your weight pretty fast.
Backing up is interesting to learn. Turning takes a bit more room - you can turn tight when empty, the front wheels scrape sideways. When loaded, you snap the hitch off the wagon trying that....
It will work well for you.
--->Paul