Having lived in the frozen northland I can assure you that not only will your toiletries freeze in the winter, but they'll bake in the summer. Exterior walls in Minnesota need insulation.
If the Mrs insists, I'd recommend insulating and sheetrocking the wall and then putting up a second wall to accomodate the inset cabinet as already recommended. You don't have to do the whole bathroom that way, just an alcove for the sink/cabinet area. While you're at it you could put in inset shelving and fancy recessed lighting in the false wall beside or above the inset cabinet
It's a lot of extra work but if the Mrs isn't happy ................. I'm glad you're the one who'll have to put up with her.