I totally understand your concern and would be worried myself if my horses were out in the cold. 20s-30's fortunately is not that bad on them, and its not been raining. Age yes can play a part, and so can where they have been living the last few years (part of the country) but remember horses have lived in the wild for a long time. I grew up in Upstate NY where a horse ranch still turned their 40 head out in the back pasture for the winter. They scattered 20 or so round bails, locked the gate and called them in when the snow (which got 7-10 feet deep) melted in the spring. They rarely lost anything but a young foal or a very old, ill horse. I hope that makes you feel a little better.
I would definitely require this boarder to supply you with a weight equivelant of "a splash" and the actual poundage of hay they provide daily. Since not doing that would be neglect on their part and you obviously don't want to have to report them, or stop paying or anything. Horses don't have a problem getting to grass under snow or dead leaves, but if they have eaten it all... I'd be more concerned with water supply. They can't drink ice. It also wouldn't take more than 10 minutes on their part to string some tarps between trees for a wind break. I hope you get it worked out.