This happens occasionally. I just either load it, or if I saved ages ago I just don't use barbers for a while and come back later, or I repeatedly try until my character shows up.
if you play as a child, if you use a MOD, that could happen.
This can happen if you are wearing headgear like helmets that cover all of your head. Try removing any headgear before getting a haircut.
as stated above, the shojo race causes this problem, this is because of the difference in height, you can try to fix this by using the console command setscale before having a haircut (try setting your scale to the closest to the normal human scale *note: you can input double values (1.5) as the scale).