Barbed wire fences are not an issue at all IMO. They are everywhere. They are not a problem at all.
On the feeder pen issue, the real question in your situation is not how high they CAN jump, but how high they WILL jump to get to a feeder.
There is no set answer to this. Depends on the place. Depends on the year.
My deer in east TX don't like fences around feeders. When I put them up, most of them wouldn't jump in. Some would, but many wouldn't. When I hunted in central TX that did not seem to be an issue nearly so much.
The exceptions are bad drought years when they were just hungry period. Then the fences were not an issue.
I learned long ago you can't reason someone out of something they don't reason themselves into.