Since Santa is often referred to as "A jolly old elf" it does seem like Santa Elves can grow beards. At least the one that is the Face of the organization. Maybe there is more going on behind the walls of Toy Central that we mere non Santa Elves are not meant to know. As for a D&D interpretation. Gnomes are a possibility. There are a bizzilion types of Elves. Why not many variations on Gnomes?
Could be as simple as the name. Santa's Elves are just that, an offshoot of Elves that work at the North Pole in Santa's Workshop. After the annual, secret and rather vicious gladiator style completion held just after Christmas, one wins out and becomes Santa and is allowed to sport a full white beard and serves as the face of the place the next year. After which he goes into a well deserved retirement and the next one is selected.