In general I think they would make a good platform, load capacity would be great and you would probably never get near gross weight so all the components would be less stressed. My concerns would be the full domestic size trucks handle very differently when empty or lightly loaded and if there is no load you pretty much get zero rear traction. My stock Dodge Cummings 2500 4x4 doesn't go off road very often but it is very twitchy when driving on washboard even when driving slow, the 3500/350 would be worse.
General size of the f350 will be a problem on tight trails but that might not be a problem, you did not say where you were taking it. I don't have an f350 but when I bought the dodge and was looking around I recall all the 250/350 series trucks from the big 3 being roughly the same size. These trucks are bigger than you think and the cab of my dodge is the same width as my unimog but with the mirrors on the dodge it is wider even if they are folded in (the mog mirrors come off and also fold perfectly flat). If the F250 turning circle is anything like my dodge then its truly crap, you'll be doing some three point turns and my dodge is a short bed.
You don't inherit the world from your parents, you borrow it from your children.
1979 Unimog 416 Expedition Camper
1974 Unimog 421
2004 Dodge Ram 2500, 4x4, Double Cab, Cummins Turbo Diesel
2006 25' Airstream International CCD
2009 Harley Davidson
Sugarloaf, Boulder, CO