There are a few things I can think of right off the top of my head.

Check the exhaust system, especially the tubes that go under the engine, and the Y that combines them. Original replacement exhaust parts have gotten very pricey, and this can end up costing several hundred dollars to fix since the engine needs to be pulled to replace with original parts. Many are replacing the exhaust manifolds with ones of a truck, and making custom exhaust that is much more affordable, and doesn't put as much heat into the oil pan either.

The early 3208 engines needed new bearings rolled in every couple thousand hours, but short of pulling the oil pan and main caps  to check them your not really going to be able to inspect them. Both the 3150 and 3208 will smoke some in the cold weather until the are warmed up good. Look for loose motor mounts. They can usually be tightened back up, but do come loose from the vibrations of that V8 CAT. Early 3208 engines also had a problem with dropping valves, but by now they have either done it, or been replaced because of it.

Short of that, do the usual oil checks (levels and condition), drive it around and try all the gears while listening for odd noises. Operate a hydraulic remote with nothing hooked to it. You should hear a rattly/squealing noise from the relief valve opening. If not, the hydraulic pump may be weak. Run it for awhile to see if the hydraulic oil gets too hot. If you have run it for 15 minutes and the hydraulic pump is too hot to touch, something is wrong.

Try the over under, make sure you can feel a speed change for each range. Then drive up an incline in over drive (doesn't matter which transmission gear, 3 or 4th will be fine) and push down on the clutch pedal while leaving it in over drive. If the seals are good in the unit, the tractor won't roll backwards until the pressure has bled off from the over drive circuit. In a good unit, this will take a few seconds or even longer. If the tractor rolls backward as soon as the clutch pedal hits the floor, it either isn't going into over drive, or the unit is leaking off pressure very fast and is going to need rebuilding in the near future. Parts are available, but not cheap.

The price of the 2255s have been going crazy lately so its hard to say. But it seems like a good two wheel drive is in the $7 to $10 K range, and front wheel assist, probably in the $10 to $15 k range.