Yes many craftsman homes have painted wood. Go to Houzz photos and type in key words to see hundreds of variations on the craftsman theme. Personally I prefer painted to dark. I think it enhances the design elements.

They may now have painted trim, but originally the vast majority were natural woodwork. Many have been painted over the years, destroying the original intent of the craftsman style. If you are interested in authentic craftsman and not trendy stuff, do a Google image search for vintage craftsman interiors. Craftsman was all about simplicity and nature. Simple designs, natural woods, and earthy colors.

Your house is a new house. You can certainly have craftsman in painted. While some purist cringe at any painted wood, at the end, the British, for example who have many centuries on us, have painted any wood they have wanted. It is still your house. and it is cheaper.

We just built a craftsman style home, and we added a lot of painted wood because that is my preference. I tried to have a lot of natural stained wood accent pieces, such as on our beams, eaves, several bath vanities, furniture, and of course our floors. There are lots of other places to incorporate the craftsman elements, such as in your lighting and hardware. Good luck!!

We deal more with the tile elements in Craftsman Homes, but my inclination is that the natural wood is more in keeping with the style and period. Good luck with your project. Jim/ Cottage Craft Tile