It absolutely depends on time and place. In today's world of mass-produced textiles, it's hard to imagine just how hard it was for pre-industrial Europeans to put together a personal sense of style, but it seems like hair—both head hair and facial hair—was often an important part of a person's identity. The Merovingian kings had been famed for their long locks of hair, and when they were deposed, their hair was often ritually cut. In contrast, Charlemagne's contemporaries took careful note of his mustache—a style of facial hair more closely associated with Roman ideas of barbarians rather than Roman ideas of emperors. Across the Channel in Britain, the 600s witnessed a feisty controversy over whether monks should have the heads shaved at the top (as in Rome) or at the back (as in Ireland). And in Viking-Age Scandinavia, Harald Fairhair got his name for finally using a comb after consolidating the Danish kingdom, whereas Sven Forkbeard was known for his distinctive beard.

These are, however, high points in the documentary evidence. Most people weren't kings, and so there was little reason for medieval historians to record what their facial hair looked like. The archaeological record, meanwhile, typically destroys hair and any useful traces of hair styles. And even for the kings who we know something about, our evidence is often frustratingly vague—what made Harald's hair so fair? and how did Sven fork his beard, or did it naturally grow in some forked sort of way?

If you're interested in medieval facial hair, I'd absolutely recommend the title essay in PE Dutton's Charlemagne's Mustache and Other Cultural Clusters of a Dark Age (2008). It's a great read, and most public and university libraries should be able to get you a copy.