First, enable the "Invincibility" code. Go through the Snow Gate to Icy Lake and find snowman. Make him mad. while standing close enough to keep him mad, but far enough so that he does not swing at you. He will instead repeatedly throw small snowmen, which will die and drop coins when they hit you. Let the game go idle to automatically gain the coins.
To accumulate tons of coins quickly, head to the game's very first level. At the end of the level, you make a sled, ride it to the bottom of a hill, and then go through a door to end the level. Going down the hill earns you about forty coins. Do this over and over again to accumulate as many coins as you need.