Elves are like Humans; some have body hair, and some don't. Some have a lot, and others less. Elves tend not to have facial hair, and less body hair. They do have eyebrows & lashes, however. Of the few PHB illustrations, none have facial hair (not even the Half-Elves), and none but Sovelis have any body hair other than on their heads (he has arm hair, IIRC). So, in general, Elves are not a hairy race...