I've been waiting to see the views of others as it seemed to me that it was only me that the word 'caravan' was visible to.
When I look at a vehicle/trailer combo designed for conditions of poor traction the trailer wheels are always well to the rear with at east half the trailer weight on the 'nose' to bear down on the vehicles driven wheels to add traction. Basic tractor trailer stuff.
When conditions are bad enough to demand winter tyres or chains, getting and keeping the vehicle moving is the first priority and I really wonder if attempting to tow an inevitably heavy caravan is viable.
Then there's the lateral and braking stability of the caravan in snow. If it starts sliding the whole plot will be in the ditch in an instant.
Asking about the pros and cons of winter tyres and chains is one thing. To lack the knowledge and experience of them with the intention of towing seems to me to be misjudged.
I may well be totally wrong and that what is being proposed is perfectly reasonable. Please then, people with that view and experience come forward and say so - for my peace of mind if nothing else.