Edit: You guys mentioned Tolkien as the ultimate authority on elves. His elves did have beards sometimes. Círdan the Shipwright had a beard at the end of the Third Age. But, according to Forgotten Realms lore, elves have no facial or body hair.
That's a trait universal to D&D's elves in general (Forgotten Realms and otherwise).
When a big fuss is made over "elves" with facial hair, they turn out to be Half-Elves. Tanis of Dragonlance is a famous example ->