What ype of paint should I use for an outdoor wooden snowman, exterior house paint or craft paint?

Using exterior house paint is totally unnecessary. A good quality artist's acrylic paint, (such as Liquitex), will work just fine. Once you have finished your painting always make sure that you finish by sealing your work with a topcoat. I would suggest applying at least two coats. Once it is sealed you should have no problems regarding chipping or pealing no matter what the weather.