Composting toilets do not freeze during cold weather.
A composting toilet uses no water so the composting toilet will not freeze and crack like a normal water based toilet would.
The solids in the toilet may freeze when the toilet is left in a cold building.
And the urine if not removed and dumped out from the second container may freeze as well but the composting toilet itself will not freeze and it's safe during cold weather.
Also you can use toilet paper in a composting toilet.
The toilet paper will compost in the toilet just like the poop will but the toilet paper will just take a bit longer to compost in the toilet than the poop will.
Just like toilet paper can be put in a regular toilet you can use toilet paper in the composting toilet and it will be just fine.
However the toilet paper will still be visible for awhile in the composting toilet because it takes a bit longer for it to break down.
Just don't put diapers, tampons etc into the composting toilet because diapers and other things like that will not compost.