We already cleared that mudrooms are here for the functionality: the main purpose is to keep your house clean by having a place where to keep the shoes. So, what are the must haves? First, you should have enough storage since shoes go here. Also, do not forget to add coat racks. And one more thing:a basket for the umbrellas.
It is advised to have tiles in your mudroom, so it is easier to clean. Also, some might include a sink in theirs. It is a nice idea for gardening, or even if you have a pet.