Cat poos on Carpet but only in the Winter

Hi I've had my cat for about 4 years now. She was a rescue cat and was badly treated before but is very much loved now with us. During the winter last year she started pooing on the hall carpet. It stopped all summer and started tonight again. She was outside for about an hour and then comes into the house and poos in the hall carpet. Can't understand why she does this. Up till last week she was doing both in her litter tray or outside. I lift the poo and place it in her litter tray and she uses the tray for a while then back to using the carpet. It's definitely something to do with coming into winter time. Has anyone had any experience of this with their cats? Thanks

I have heard people say their cats do this.  I'm not entirely sure why.  Does she prefer to go outside; where the ground is soft and natural?  Is she declawed?  Does she use the same spot on the carpet each time?  How many litter boxes does she have?  Any other cats in the house?

Sorry for all the questions; I'm just trying to get a bigger picture of what could be behind this.

Hi there

She goes out occasionally in the winter but tends to stay in if it's raining outside.  This morning I came out of the bedroom and the hall carpet was clean so I thought maybe she had used her littler tray.   I let he outside but she decided to come back in.  I cleaned her food bowl and gave her fresh food and water.  I then cleaned the littler tray and just as I was finishing that she wondered through to the hall so I walked through to find her ready to poop.  I picked her up and put her in her little tray where she did a small poop.   I've had feliway spray and plug in all night, I've cuddled her in for hours a time last night and spent time making sure she is receiving plenty of attention but since this episode this morning I have now restricted her to the utility and kitchen area.  She has a nice cosy sleeping bag and her sheepskin bed so will be warm enough.   Her food and litter are in the utility area where they have always been.  

She has one litter tray that she uses with no problems in the summer time.  There are no other cats in the house and very few outside.  We are not in a busy noisy area so she should have peace and quiet.

I have spoken to the vet and she has said it's either hormonal or stress but why does it always start around late September when the dark nights come in.   She suggested Feliway and said that she can give us tablets to try which de tress them.    Her food intake increases quite dramatically so maybe it is stress related. 

Think I will try and get a urine sample and get her checked to make sure it's not an infection of any kind but that doesn't explain why it happens in winter...cats don't get UTIs just in winter months.

I'm also going to speak to an animal behaviourist to see if they have any answers.

She was rescued by a friend 6 years ago after being locked up for two weeks without food.   My friend had her for three years and gave her to me due to a house move.   I've had her for three years where she has received lots of love and attention with no stress caused by other animals or children and believe me she is spoiled so I just don't know where I'm going wrong and it's quite depressing.   I had two cats from kittens for many years and never had issues like this...they were angels. 

The strange thing is that she pooped in the littler tray the previous day so it's an intermittent issue.  Can't fathom this at all.