You know, it honestly depends on the person. If the person comes in and is rude, I would honestly prefer them to sleep because then I don't have to try and attempt small talk. If they are asleep, it avoids the akwardness. On the other hand, if it is someone that always comes in and I chat with regularly, I might be dissappointed to miss out on our talking time.
Honestly, in your case, I wouldn't worry about it. If you have been getting haircuts from your barber for 15 years, they are probably already comfortable with you and understand your situation. The other thing is, getting your haircut, especially for men, is actually a very relaxing time and with all the white noise from the clippers, it would be very difficult not to fall asleep. As a barber, I would take it as a complement because they have you so relaxed and you are trusting of their work, that you are able to sleep!
So, ultimately, I wouldn't worry about it. Take the extra time, sit back, relax, and catch the extra zzzzzzz's. If your barber doesn't seem the least bit irritated with you sleeping, chances are high it doesn't bother them. And if you are getting a good haircut, you probably aren't a jumpy sleeper, which makes it easier for the barber.
Hope this helps. Take care!