I think that one has to assume the worst case scenario on this unit, i.e. it was running hot when it rolled into the lake.
I would point out that it has a cab with an AC cooler on it, with an enclosed cab. Someone went to substantial extra effort on this unit.
On the bright side, none of the glass is cracked, which suggests the ROPS wasn't hit hard. On the other hand, the engine photo looks as if the battery case is folded toward the engine and the engine is folded toward the fuel tank. I'm having trouble imagining how you could bend things that way, unless the tub is bent (doesn't look it), or a tree fell on the engine compartment.
As others have pointed out, if the engine inhaled water, it is probably a write off at this point, but the hydraulics might be OK. The fact it cranks over suggests at least some of the interlocks are working. (The fuel solenoid may not be...)
I'd consider buying it for parts. But you would be a lot of parts shy of a running 1850.
I have the 1445, and I use it routinely on 25 degree slopes. More than 25, I run up and down them perpendicular to the slope, as I am no longer comfortable with my safety zone. (I've never tipped mine, and I would like to keep it that way!) Over 20-25 degrees on our hard clay/gravel slopes, the tractor does have some traction issues. I have been fence sitting about going with forestry chains, or duallies, $1200-$2400 respectively. PT recommends against dualies on the 1445, but are OK with wide singles e.g. turf tires.
One comment on the 1850 for brush cutting; the 1850 has a three rotor brush cutter. This keeps the mower close to the tractor, and reduces the tendancy of a heavy mower to torque the tractor downslope in a cross slope cutting method. However, the rough cut mower is not really a brush cutter, more of a heavy grass/weed mower. Check with the factory, but I was encouraged to go for the 1445 with its 72" two blade brush mower, because I wanted to cut down shrubs. I can say that for mild (20 degrees and under) it is a tank, mowing anything and everything in its way. I mowed a burned out tree stump 2' x1'x2' by accident on Friday. Unintentionally! It had been a horse toy and the ponies had left it in a pile of weeds. However, on steeper slopes 20-25 degrees, the mower is a long way out from the center of mass of the tractor and has a tendency to torque the tractor down slope as the wheels slip. As a result, I mow the steeper slopes perpendicular to the contour, i.e. up and down hill, as I find it easier than compensating for the slip and worrying about finding a woodchuck hole on the downhill side.
If you have slopes, I think that Power Tracs are great machines. I can't imagine doing the work that we do with anything other that a PT or something like the swiss version.
If you plan on doing a lot of brush cutting, I would consider a secondary oil cooler for the engine, and a bigger fan on the hydraulic cooler. They are relatively cheap insurance against getting too hot. I know what it is like to brush hog in Michigan summers.
All the best,
Peter