Lending policies will vary.
But back when I was a Realtor, most places would only loan money on land with a 50% down payment, I have heard that loans for "land only" are very hard to get and almost impossible anymore.
2,000.00 for a Fencing 4 Acres?
10,000.00 for a Barn?
I need to move to your area
Seriously, I think someone is misquoting or would build something so cheap you would not want it nor would it be be safe.
It cost us 1,000.00 to fence 1 acre and we did the labor ourselves.
I built a deck on the house last year and it was 1,500.00 for material only, we did labor, a small deck only 12'x16'
You also need to think about how to get the water to the Horses, is it a creek (fencing problems) or will you need a pump? If a pump, electricity?
Then you have property taxes.
What about liability Insurance.
Maintenance on the Fence.
Maintaining pastures, reseeding, weed control, bug control, etc.