I have always thought long hair was the norm for many "barbarian" races, such as the Vikings. First of all, they lived in the North, in cold climates, and long hair and beards protect the head and face from arctic temperatures. I have read that in cold climates, 80% of a person's body heat is lost through your head, so protecting your head is very important in cold weather survival.
Long hair has been a feature in cultures all over this planet for millennia. The Arabs and Orthodox Jews both have such traditions, as do many Far Eastern cultures. The Hindus also have such, but since they're descended (more or less) from Indo-European immigrants from the north, one can argue that "practicality" plays a part in that.
Historically, short hair (in cultures around the world) has often been the mark of children or slaves.
As to long hair in fights, Conan was a professional fighter, and there are techniques for dislodging a person's hand from your hair. For example, if a person had a hold of Conan's long hair in the rear, where it was not attached to his scalp, this is a simple matter of twisting your body into the person. The person is then dislodged by close quarters fighting techniques such as smashing your elbow into their face or neck. Unless you grab a person's hair close to their scalp, it is not going to be very effective. Grabbing a person's hair close to their scalp can happen to people even with shorter hair. If someone grabs your hair close to your scalp, those schooled in the martial arts know to take both hands, trap the grabbing hand(s) by pushing it down very forcefully into your own scalp. You then lower your center and spin violently inward toward the aggressor while standing straight up. This is usually more than enough to dislodge their hand, and it can cause damage to their shoulder or even break their wrist. Also, I have always felt that Conan's hair was long, at least shoulder length. I have interpreted Howard's descriptions of Conan to indicate that this was the custome of the Cimmerians and perhaps even a mark of pride or prestige in their culture.
Robert E. Howard's historical Gaels, the "descendants of pure-blooded Cimmerian clans" were usually portrayed by REH as having shoulder-length hair, if not longer. In the antebellum American South and on the American frontier, long hair wasn't uncommon.
Both myself and Painbrush (he died a longhair and I rocked it for over 20yrs) addressed the "long hair in a street fight" question. I was in about 20 street fight fights after my hair got past my shoulders. Never lost one fight.
Conan's hair was long and wouldn't be any serious detriment.