Composting toilets will work in cold climates but the composting toilet should be in a heated area for it to work in the winter.
If the composting toilet is outside and it gets cold then the composting process will stop until warmer weather arrives again.
So if you're using a composting toilet just be sure to keep it in a heated area such as in the house where it's warm or in a garage where it's warm.
As long as you keep the composting toilet warm it will still compost.