Hi Lady Farmer,
Below are the pros and cons of Asbestor sheet and Steel sheet for roofing.
In general Asbestos sheet is considered hazardous for health as when time passes a very tiny particles keep coming down from the sheet and that is considered dangerous for the heart and causes breathing related disease. Also very extra care should be taken when you are taking out those sheets for some reason.
Asbestos sheet are cheaper that steel sheet but seeing the risk of health I wouldn't suggest this. Also there is chance of breaking when time passes or while installing the sheet.
I feel steel sheet is the way to go particularly when now steel sheets are coming with quoting (blue or green) so their life has increased and they also resist heat. You can for sure use them for rain water harvesting that you can't do in Asbestos sheet as some tiny particles gets mixed with the water.
To make the home more cooler in the winter you may apply husk or straw over it. Of course, steel sheet is costly but seeing its benefit I recommend this.
I hope my answer would help.