I mean, I understand that shoes get dirt on them, but actual mud often enough to decide that a room should be named after it?
I digress.
A mudroom should serve a few purposes: somewhere to take off your shoes, somewhere to hang your coat, a possibly also a drop zone for the mail, or your purse, or all of the kids’ school papers.
It doesn’t always have to be a room, in this case it’s more of a functional hallway.

You come in from the garage, take a right into the walk-in closet to drop off your coat and shoes, and then back through the hallway with a full storage system built-in for dropping off an umbrella or plugging in your phone at the charging station.
The bonus with a storage system like this is it also serves to house extra light bulbs, or cleaning supplies, or that 16-pack of paper towels you picked up at Costco.