Literally takes their shoes off inside the house, or takes them off outside, and then steps in?

Is a "mud room" a Canadian thing?

I've heard it called mud room or front foyer.

Widely used term in New England in the US as well. For me, it's not a literal room but a tiled extension to the kitchen where I take off dirty shoes and so forth.

Takes their shoes off in the "entrance" (or mud room maybe, though I've never known anyone who calls it that) of the house, which is generally a small tiled area immediately inside any doors that lead to the outside. Shoes are left on the tile (or a mat / plastic shoe thing) and then folks walk without shoes from the entrance area into the rest of the house.

I think it's a good idea.

Leaving shoes outside doesn't work unless the outside portion of the entrance is well sheltered. I've definitely seen it before in condo buildings where there will be a mat and boots neatly lined up in the hallway. Seemed strange though.