Sounds a lot like gas colic to me. Having multiple horse presenting the same would make me want to look at the common elements in the effected horses diets.
If it were me I’d*start soaking the horses hay, and see if anything changes after three days on soaked hay.
To soak the hay… Put hay in a muck tub, submerge with with water, let it soak for at least four hours (or over night), then drain.
Soaking hay can remove mold or anything else that may be on the hay. It also adds water to the horses diet.
Many horses tend to colic in cold weather or during abrupt temperature changes. Some theorize that temperature change can effect a horses intestinal flora.
Giving a probiotic to horses during the winter months can be a good idea.
Dry winter air is dehydrating. A horse should drink more in the winter than in the summer.
Some horses drink more when given warm water in the winter.
Also look at the water source to be sure there is no contamination. Water quality can be tested.
Beat pulp can have mold problems too. If all bags are from the same manufacturing run, they may all have mold.
The same goes with moldy hay. Just because it comes from the same farmer it does not mean that it’s all cut, baled, and stored the same.
Some hay farmers who switch to using propionic acid grass hay preservatives, have know idea how to apply it properly. I’ve seen entire barns with multiple “mystery” colics turn out to be caused by over application of propionic acid.
Propionic acid will retard mold growth, and the Propionic acid will eventually dissipate in concentration in the bale. But it’s not meant to preserve hay baled at over 19%-20% moisture content. Some hay farmers will try this and the result can be bales that will mold in different, more difficult to detect ways, than grass hay baled without preservatives at 15%-18% moisture content.
Look at the hay, water, and the beet pulp for mold or contamination. Mold testing is available too.
I’m not saying that’s the issue, just that it’s the first thing I’d look into based on my experience with mysteries like these.