I would do tile in a mud room just too much mess for hardwood.

My neighbor just put wood look tile floor in her kitchen. It is amazing, you cannot tell that it is tile!!! It matches her wood floors through out perfectly in color.

I would do tile in the mudroom, and kitchen, but that's me! :-)

Look for a wood look tile that would be in the same color family as the wood stain on your other floors, or match the stain to the tile to get a cohesive look.

Or just go something totally different in tile, but tile the mudroom.