You don't need a mudroom
A functional entryway needs three things: somewhere to hang outerwear, somewhere to drop keys, and somewhere to park shoes. You can fit all three in 3 feet of wall space.
Wall Mounted Coat Hooks on Amazon
Shoe storage that works
A slim shoe rack that fits behind a door or against a narrow wall keeps them off the floor without eating up square footage.
Seasonal rotation
Your entryway should only hold what's in season. Off-season gear goes into bins under the bed or on a closet shelf.