Ah - a mudroom. I do not have one and would love one, but they don't come in my neighborhood
A saw a 2-3 tiered boot/shoe holder thing - it has a base on the floor with 2-3 rotating circles with clips to hold boot and shoes but would work well for damp mittens and hat too.
Those over-the-door shoe holder pockets are good for storing dry hats and gloves
A big floor matt with good absorption is nice too