My bulldog has already had a heat stroke...in December..
He was caught to long..
Right now I'm torn on putting one on him when the temps heat up because of this, I ran him without one a couple weeks ago because it was so muggy and had no problem, I guess it just depends on the situation, like if he's gonna be riding on a truck or 4 wheeler or walked the whole hunt. Normally I wouldn't ever run a catchdog without a vest, but I have this to factor in.
As far as the vines and briars go, bulldogs are gonna get their face cut up in vines, vest or not. I wouldn't worry about that, and if they do get hung up, oh well a missed catch, you'll get em again...
If his health is fine, get a good vest and keep it on him during hunts....like Chris said, the good outweighs the bad.