In the original game these snowmen appear in the fourth stage, Artic Caverns. They're stationery enemies which constantly throw snowballs from a distance. At the beginning of the stage you can throw snowballs back at them, but later you'll have to rush at them to hit them directly.
They appear again in the Arcade game, where they have a similar attacking pattern, though they're helped by a strong wind which pushes the player back. Later on they're able to roll around to hit the player.