I know I'm not a mom yet, 3 weeks to go, but I have given riding lessons to a lot of small toddlers. Usually around 2 - 3. Quite a few of them do this, as well as my previous employers son.
In general it is a shock tactic to try and get attention. I know splashing them in water or just letting them be sounds horrible, but breathing is actually not a voluntary action. Yes, they can hold our till they turn blue and sometimes pass out, but once they pass out the body's natural defense systems kick in and they will start breathing on their own again.
With my boss's son I just usually left him. She had the habit of leaving him in our care while we are cleaning wounds, etc on the horses, and he would do this while we get busy and can't give him the attention he wants. As you can imagine, I can not splash his face in water when I am in the middle of a field trying to keep a toddler from being trampled by a high strung horse in pain, so I just did what I could, I ignored the whole tantrum, no matter how scary it got. Yes, it scared the living daylights out of me, especially the first time he did it, but when I realized what it was all about, I just let him be. Luckily I was one stubborn little monster as a child and I can fully remember the extent of my own tantrums, which involved screaming till the veins in my eyes popped, so I know how stubborn kids can get when they want something their way. ( I threw a horrible tantrum one day when I was around 3, because I wanted to fly from Walvis Bay in Namibia to Pretoria in S.A with the granparents on their return flight. Despite the largest hiding of my life my poor parents had no choice but to give in in the end, as I just kept screaming blue murder for almost 6 hours straight. And scarily enough I can remember the determination of it all till this day, as well as the thrill when I got my way in the end. Yikes!)
When you should get intervention though, is if he goes into spasms, or if he does this frequently. It might indicate epilepsy or a nervous system problem which is a serious issue if left untreated.