I have found what appears to be an exact match of this treen Georgian style salt shaker described as 18th Century Colonial (and which sold at auction, with a matching pepper shaker, for $750.) I am not sure this piece is that old-- I think perhaps mid- to late-19th century--but certainly it is very finely made, lathe turned, of a beautiful hardwood. I have also found "muffineers" of the same style, used for sprinkling cinnamon or sugar on muffins; I believe those are distinguished by an even denser pattern of holes, but surely this could be used for that as well!
The top is threaded, easily screwing off to fill the shaker. I have not touched the wood on this piece, which is in excellent antique condition, with just a bit of wear around a few of the shaker holes, as pictured. On its underside is the remains of what I think was an old label. It measures 5 1/2" tall x 1 3/4" in diameter at widest; 1 1/2" across at base. What a lovely thing to put on the table and pleasure to use!