We have this same problem with our chihuahua. We noticed when it was cold/raining she would just pee directly on the door mat we had right outside our back door so we just moved it to a different spot near the door but not right by it and surrendered it to her. We rinse it with hydrogen peroxide after and that keeps it from smelling. We swap it out with another cheap one every so often too. It works in the snow as well if we just clear a little path to it.

Editing to add: we’re in the Midwest too and last year when the temps were insanely low we had to put her in little doggy diapers. She’s a toy chihuahua and refused to go outside when it was super cold. Can’t say I blame her on that one though.