For your needs, the F-250 7.3L is the right truck.
I've got one. 380,000 miles. Still running strong.
Make sure it's the 7.3L. Made up until the first half of '03.
Don't sweat the mileage. I'd jump at a 150,000 F-250.
Yes, you need the 4x4. Farm, horses, mountains. 'Nuff said.
The GM suspensions aren't great for farming (less suspension travel). Cummins engines are great, their trannies are questionable.
As I understand, the vast majority of farmers favor the Ford.
One more thing- consider the wheelbase. There is a big difference. You have conflicting needs on this one. The mountainous driving makes me want to recommend a shorter wheelbase for maneuverability (short box, not crew), but the 4 horses are a heavy load, and the longer wheelbase will be more stable with the heavy load (though it will turn like a freight train). A dually will be the most stable.