Yep, when the horses have to be stalled because of bad weather, they get hay nets as well. My one gelding will grind his into his bedding and then poop on it if I don't use a net. Pretty obvious he's not starving if he does that!
Pasture doesn't grow very much in the winter anyway, so it's going to be eaten down to nubbins. Where in VA are you located? I'm in south central, east of Lynchburg.