IDK about other kinds, but Ricean vampires would have face, head, and body hair at the length and placement it was when they died (the texture and color of the hair does change slightly, and hair dyes would not remain permanent). 

Jesse mentions being groomed before she’s turned. So those stray eyebrow hairs wouldn’t keep growing back for eternity.

There would be a nightly choice of shaving the face or not, if one had a beard when they were turned, and it would only grow back to the length it was the night they died. Which is partly why we never see movie!Louis trimming his sideburns, they won’t get longer. He could shave them off but they’d grow back. 

[X] ^Lookit this bearded cutie trying on his fangs awwww… ❤

Lestat doesn’t mention having or being able to grow a beard. 

I answered this a little more in depth here.