Anyone read Laura Palmer's diary? (White horse question...)
The white horse was also shown in part two when Laura goes away screaming.
Also remember that the casino where Dougie hit the jackpots was the silver mustang (which is a white horse). I read a little about that and it seems that actually the white sands (the place where the atomic bomb is blown in part 8 and was blown in reality) is one of the places where horses lived freely (the meaning of mustang). Probably why they wanted to remark the sound at the end of part 8.
Moreover, when Coop turns to the diner called Judy's, there is a mechanical white horse in the outside.