I don't think pawing is a "wild horse thing;" since when do wild horses get grain? The only time they have to paw to feed would be when there is snow cover on the ground, pawing at any other time of year would just dig up the grass they are trying to eat. Pawing might break ice over a frozen water hole, but you generally don't see horses pawing while drinking, except perhaps in play (a horse that paws in water usually follows up by rolling in it!).
Pawing is a behavior that many horses exhibit when they are anxious about something. Feeding time is a very anxious time for most horses, they often show behavior then that you don't see at any other time. I know several horses that stand on three legs, with one foreleg raised and sharply bent, while they are eating grain (looks like a variation on pawing to me). Some anxieties are very deeply rooted, having begun way back in the animal's past. There may be nothing in the present arrangement to make an animal anxious, but it continues to get wound up because it always gets wound up, a sort of self-perpetuating loop. When I think of horses exhibiting feeding-time anxiety and food aggression, the most extreme examples that come to my mind are also dominant animals that nobody they live with now would dare to challenge. They may not have to worry now, but somewhere in the past there was a horse that would take the food away (maybe even the mother) and the pattern of getting stressed out at feeding time became set.
