cat on my door mat

I have georgie, my 10wk old puppy, and i have 2 cats that are 4 and 3. My 4 year old cat is blind and has been since birth. I can tell winter is here as she wont go out in the winter. Not sure why, as in the summer you cant get her in! She has started her annual peeing and pooing on my door mat inside the front door. She hides in the day time too and if i put her out she just miows at the door to come back in.

Does anyone else have this problem with cats in the winter? My 3 year old cat is not like this at all, he will go out in all weathers.