Vestibule.

If it is a formal external architectural element it is often called a portico.

Except that a portico is roofed, but open to the weather, as a porch.
The vestibule was reinvented during the 1970's oil crisis as an "airlock entry".
The word vestibule literally means cloaking room, like where you donned your overcoat.
It is always understood to be a chamber, not a porch, stoop, atrium, veranda, or piazza.
Casey

For all the modest 1880s-1920s houses I have owned/renoed here, it was the standard setup--an eight foot hallway with a row of coat hooks and another doorway at the end. Usually, the second door had long since been removed. From the 1970s on, virtually every reno removed most of the hallway and all the rest of the first floor partitions separating living and dining rooms with the kitchen at the rear.

In architecture the term "vestibule" is taken from the Roman house element "vestibulum" which was not a room in the house but a small alcove open to the street containing the front door. The term was later used to denote an entry court of some kind but today "vestibule" refers to any small space leading to or exiting from a more important space.

The term "portico" historically refers to a formal entrance element with a roof and columns of some kind but today it is used even for some enclosed entrance elements if the underlying portico structure is evident rather than integral with the design of the house. I suppose such an element should be called an "enclosed portico" but then no one says "enclosed vestibule".

Yes, vestibule is what I was thinking of.

The house I grew up in, and the house Mom lives in now, had provisions for EXTERIOR vestibules that were erected in the winter around the front door.

The cleats into which the vestibule walls locked are still in the woodwork in both houses.

While digging through the basement in Mom's current house, I found parts of what I believe to be the old vestibule, and I'm thinking seriously about trying to resurect it.

I recently visited Halifax, Nova Scotia. It's full of beautiful Victorians, many with original small glassed-in front porches. Up there, they call it a "storm porch". Makes sense.