We have the first one which my daughter has sadly grown out of. It got loads of use, we purposely bought one that would be too big so it would last a couple of years.
In the winter she wore it in the snow with several layers underneath. In the summer she wore it with just one layer under. At a festival when it was blazing hot but had been raining she had it unzipped and the arms tied round her waist so she wouldn't melt, but could still sit/crawl/fall on the wet grass.
It scrunches up small so we just kept it in the bottom of her nappy bag.
I 2nd the advice of putting it over the wellies. It won't stay there, but there's a chance the feet will stay dry.
In fact with our "summer" holidays coming up I might buy her another.