REPLY: It sounds like from here that your horses are doing this head swinging because it releases endorphins in their brains and now they're hooked on the endorphins and can't stop. We see this kind of behavior in horses that have been stalled extensively at some time. Overly confining a horse in a stall is very bad for horses, and in their attempts to cope in the non-natural environment,
they begin such behaviors as weaving (swinging the body back & forth rhythmically), pacing (what that other gentleman was referring to there), cribbing (sticking out their heads and chewing on wood), "wind sucking" (which is like cribbing but without their mouths connecting to the wood), and head swinging like you are seeing there in your horses. All of those behaviors, done repetitively in the confined area, begin to release endorphins in the horse's pleasure center of their brain and that
works to reduce their confinement stress, but habitually. Before long, they then get "hooked" on the endorphin release and the habits become very addictive and very hard to break, because it's now an addiction. Here's a link on my web site about cribbing, FYI, but all of these behaviors have the same root and same result:
These behaviors do not ever happen in the wild or with horses that are kept "naturally" (living outdoors 24/7, not stalled). They are man-made-created problems via over-confining (jailing!) a horse which is a herd animal that is meant to roam -- often moving up to 20 miles a day, just grazing!
So...that's what you're seeing there, I'm sure. The only advice I can offer is not to confine them in smaller spaces like stalls, and clearly since they are doing it in the paddock there, that is probably too confined a space for them, with this habit. Turn them out into a larger pasture, with access to grass/hay 24/7 and you should hopefully see them stop thinking so much about the addiction and maybe over time they'll let go of it. Or maybe not.
These are real hard habits to break in a horse once they learn them and then get addicted. But reconfine them in a stall and I can pretty much guarantee you the habit will return/remain.