I don't know the visages of past presidents well enough to know if this carving represents one or not, but to my eye he looks more like a barber, or a sailor, or maybe an antiques dealer! Great face, great old folk carving whatever the case, with a wonderful warm dry patina. Late 19th/early 20th c. I would guess, and even better in hand.
4" x 1 5/8" x 1 1/2". Great antique condition, with general wear all to the good and a great warm dry patina.