Utility/Mud Room
In reworking the door out to the back stairs and rear garden the goal might be a look like this though with a more period appropriate door. This room has vertical rather than horizontal wainscoting but along with the ceiling and floor moldings it is very effective. EDIT: The door frame also -- as an ensemble it looks in keeping with the rest of the house.
Although we don't need a dog bed we do need space for the cats' food and water dishes and two litter boxes. Preferably configured in such a way that litter doesn't scatter all over. Also the lower drawers in this room would be a good size to hold basic hand tools. EDIT: some hand tools will probably be in the basement, but there should be at least two tool drawers in the utility room.
Possibly some type of bench, with storage underneath, under the enclosed porch window. EDIT: presuming that the window will be retained when the porch is reconstructed; do you have thoughts on this? In addition to coat storage, cat's dishes and litter box, cleaning cupboard and tool storage, there needs to be space for the freezer.
The walls of the enclosed porch are horizontal wainscoting as in this picture. Keeping in mind the need to insulate, etc. it might be nice to retain them. EDIT: if the entire porch is to be reconstructed then we would retain the wainscoting on the wall facing the kitchen only. The other walls could be something that looks compatible.
There will need to be some kind of hanging storage for winter coats, boots and other outdoor clothing. EDIT: This room will be the main location for keeping winter clothing. The coat rack in the front hall will be for guest's coats. That suggests 8-10 hooks at least, and floor-level storage for several pairs of boots.
Though there's no need for a free standing hutch in the mudroom, I do like the idea of a shot of color as opposed to everything being white or beige.
Q