The barn is almost in a category of its own. It doesn't follow normal follower deployment rules, and unlike the pig and builder, the barn exists on its own. (In fact, it kicks followers off the farm. Only the pig can stay if it belongs to the same player as the barn.)
The best answer I can think of is that the barn can be counted as a follower by it's ability to exist by itself, but is a special figure because it cannot do the things that a follower can do (cannot be deployed to the city of Carcassonne, cannot use magic portals, cannot be eaten by the dragon, etc.)
Yes, I just said that barns cannot be eaten by the dragon. I feel a little dumb for not noticing this before, but it's right there in the rules (very last sentence). So getting back to what the dragon eats, he doesn't eat all non-neutral figures. He eats all followers, pigs, and builders. This gives the barn an EXTRA quality that neither followers nor the other special figures have, further supporting the need for it to exist in a category by itself.
Getting back to the original question of this thread, which followers are considered knights?
Followers: small meeple, big meeple, mayor, wagon
Definitely the small and big meeples are knights, but what about the mayor and the wagon? I don't think anyone would say that a wagon could be knighted, so either only knights can escape via a cloister/abbey, or the rules need to be changed to say that followers can escape, thereby including the mayor and wagon which are not knights.
Of course, the wagon is presumably more than just a wagon. According to the introductory paragraph, the wagon also includes the merchant who is tranporting his/her wares in the wagon. If the merchant could be permitted to escape with his wagon via the cloister, everything would be fine, but if the wagon hinders the merchant's escape, the player would have to complete the city and escape to an adjacent but unfinished feature. Or perhaps the wagon can escape to the cloister if the cloister is unoccupied and unfinished?
We're building quite the list of things that need official rulings.