I bought a green Army surplus sleeping pad and cut it down for a cafe' racer seat on my motorcycle, then shaped it and covered it with vinyl. It worked great.
It will also work on a saddle, as will a modern exercise mat, try to find a used on at the second hand store, they are expensive new.
Glue it on well first then sand the foam to shape it. Use weldwood contact cement, spray upholstry glue isn't strong enough.
Covering with thick vinyl is a pain around the nose, it can be done, but not without folds. Maybe a heat-gun will make it stretch enough, but I didn't try that.
I would use thin leather.