Yes they do But I have gone to our locl Farm and Fleet store and now some halters are labeled both for mini donkeys and mini horses The one I have says Mini horse Average~! This also has an adjustable nost piece and is nice and heavy duty one... But here is a place where you can order a halter just for a mini donkey
My favorite ones are the Hamilton brand halters - regular horse ones - that have the brass fittings. They are soft, but heavy duty and very durable. The best size is "Pony" for the adult minis (believe it says average mini donkey on the lable too) and there are weanling and colt (regular horse size) ones that fit the bit smaller adult heads. There are mini horse Hamiltons too, not sure how the sizes run on those. I have a weanling and a yearling one, and they are VERY tiny, but super nice halters. They make awesome summery bright colors too. I think State Line Tack carries them and Ozark Mountain Mini Tack too.