There are three ways to obtain these valuable-looking pieces of lumber. Mayor Thomas will come by your farm on the 2nd of Winter and ask you for a piece of White Grass or some other hard to get item. If you get the item he requests by 7PM on the day he asked you, he will reward you with a piece of Golden Lumber. Alternatively, Gotz will sell these for 100,000 G each after you have collected 999 pieces of regular lumber in your shed. The last one is having a 50-59 streak on the goddess' new year game.