It sounds like you are talking about something that my horse does as well. The only difference is that my horse does it whenever she gets over excited, or hasn't been out in a day. She runs around, and when she stops, she throws her head up, and exhales really hard through her nose, and makes a snorting type noise. I would describe it as a hard blowing that sounds similar to a snort, but more powerful because of the force of the air being pushed out of the nose. She does just a normal snort when she's wary of something, or something has spooked her a bit. As far as I know, its just something she does. She has no problems or anything, she's just giving a bit of attitude, and making her presence known. She's an Arabian if that makes any difference. Unless she's having problems breathing, or is really snotty, I wouldn't be too concerned.