You would have to check with your town to get a true and correct answer for your county but in most places that a burn ban is put in place the burn ban almost always does include fire pits and other recreational fires.
Burn bans don't include enclosed wood stoves or fireplaces as long as it's operated in a correct manner.
I've known some towns that would let an enclosed fire pit be burned during a burn ban and others they would tell you to put the fire pit fire out.
Most times you'll just get a warning to put it out but then the next time they'll fine you and make you put the fire out.