If you're good friends with him, on the 2nd of Winter Mayor Thomas will come by and ask you for a request. Seems as though he needs an item and he'll be very grateful if you could keep a hold of it until 7:00 pm that night. Thomas will ask for various winter-type items like White Grass, Diamonds, Truffles, Golden Eggs, and Moonstones. Even a Bracelet! If you don't like what he's asking for and you've saved that previous night, reload your game and when you talk to him again he'll ask for a different item.
At 7:00 pm that night the Mayor will come back for the item. Give it to him and he'll give you a piece of Golden Lumber. Why? I have no idea. If you put the lumber out in your field you'll kick up the fairly mean Golden Lumber event. You can't ship it to Zack either. The only thing to do with it is put it in your Shelves next to your refridgerator, or sell it to Won.
Mayor Thomas won't come to your front door in the morning if there's a storm or it's snowing on the 2nd.