I have the same issue with Izzy with the rain - she'll go outside but needs to do her business under cover. I can only imagine how she's going to be when the snow starts to fly around her in a couple of months. We invested in a doggie house that we are going to put on our deck that's big enough and we'll put pee-pads in their and set it right out front of our patio door and hopefully Izzy will get used to that and do her "thing" in there. I'd post pictures of the doggie house but DH has yet to put it together. It's large enough for her to move around in but then again Izzy is very small. Good luck - and let us both keep our fingers crossed since we are both in the same boat.
