I'm sure I've seen both used, but I'm not sure which is correct.
Readers are familiar with certain patterns and sayings, so context can really help decide. E.g.,
I'm washing his hair v I'm washing his hairs. The second instantly looks odd, although it's saying practically the same thing. Here, though, readers are in constant contact with 'washing hair' not 'washing hairs', so the latter has that aytipical-usage feel with them.
Also:
He's splitting hairs v He's splitting hair. Splitting hairs is the known idiom (arguing over tiny details), 'split hair' is too ambiguous and alien to the reader when it comes showing arguing over those details: hairs would be the choice here.
With his 'arm hair rose' v 'arm hairs rose,' it's a conundrum. Mostly because they're showing the same action, but with two phrases that, right or wrong, are familiar to readers: his arm hair rose, his arm hairs rose. Both could potentially work, but the question is: should they work?
Whether in fiction or away from that in natural conversation, 'His arm hair rose' isn't really a familiar phrase on the ear, not compared to, say: 'the hair on his... *insert body part here* rose'. So the first sounds a little odd on the ear no matter how noun is worked.
I know that brings in questions on writing not being original if only familiar phrases are repeated, but sometimes once the familiar is known, that's when you can get creative and use it to suit your style:
His arm hair/s rose
The hair on his arm rose
The hair on his arm rose, shivered, then gleefully tried to leg it with a "Feck no, you're on your own here, mate
" cry.
And so on until you get the right feel.