If worse comes to worse, a new motor could run $1500.
Jump the oil cooler fan directly to a battery to see if the fan motor works. They are notorious for just blowing a fuse and/or the temp sensor that triggers it goes bad. If the fan motor is good, you can wire it to a switch and manually operate it(that's what I do with mine). If the fan motor is broken, $50-100 repair.
Hosed can be had from Surplus Center, farm stores, etc.... for not too much. However, some are custom lengths and not much room to leave a bunch of slack around and store bought come in 2' increments.
Get it running and warmed up for 20 minutes. Drive it around. Stop moving and turn the wheels lock-to-lock a few times to make sure it has full articulation.
Check the oil in the hydraulic tank and look for discoloration, dirt, etc...
Move the FEL fully many times.
Drive it up to a tree, push against the tree with the bucket, FEL, etc... and at full throttle see if you can spin the wheels or stall the motor. I can spin my wheels with turfs and sometimes stall the motor. If the wheels don't spin and the motor doesn't stall, there could be a chance that the wheel motors are just passing through fluid and not triggering bypasses, etc... its really kind of a feel thing.
They do not have the traction and lugging capabilities of a conventional tractor, so it won't be able to pull much. But it should accellerate to 8mph both forward and reverse eaily for mowing/tram speed.
On a flat level surface at full throttle with no feet on the pedals, the tractro should not creep in one direction or the other. It should hold still.
That is an old unit. It should have the hydroback cable pedal control that uses a cable operated by the foot treadle to move a lever on the variable volume pump connected to the engine. With the tractor off, operate the foot treadle several times in both directions to make sure it moves freely and you can't feel any binds or grinding.
Remove the access panels on the sides of the tunnel in the foot wells and look at the treadle assembly and see if it has bee greased regularly or if it is a rusty mess. Also inspect the ball joints on all of the articulated joints. Bounce the front and rear of the tractor up and down and see if it flexes up and down in the middle joint. It should not. If it does, that indicated either a loose joint that can be tightened with a large wrench (not a problem) or a worn joint that could fail ( a big problem).
Inspect all of the ball joints on the steering rams. You should be able to rotate them with your hands.
Does the unit have the quick attach feature or are the attachments connected with pins? The quick attach is worth its weight in gold and I wouldn't have a unit without it unless the unit was going to be dedicated to one task, or switched over once a season. I have to change implements often, so I need it.
That's about all I can think of. Good luck.