Yes mares cycle the same at the track as they would do at a farm in a field.
“Controlling” their natural cycling during breeding season is a tricky question because as LaurieB said, “depends on the mare”. In my personal experience breaking/starting and training at the farm, which I also bred and foaled a lot of mares on. I never found “mares/fillies” to exhibit behavior during the breeding season that made them difficult to work with. There was the odd exception but never so difficult that I had to resort to meds to keep the filly/mare in training.
I dealt with it on the ground and on their backs. Kept their minds on other things as best as possible. I have never found mares/fillies that I worked with as sport horses to be/get difficult during the breeding season. Guess I was lucky and or my idea of being “difficult” is different than others.
None of the fillies/mares that I had at the track were ever given Regumate. I look at my vet bills closely, lol.
As pointed out in a number of articles on the subject. There is no guarantee that Regumate will give the desired effect. According to this in an article on the subject. It could have the opposite effect.
[I]"Many people turn to giving their mares the drug Regumate. This is a progesterone that mimics the hormonal profile of a pregnancy so the mare doesn’t show in season. It eliminates problems with excessive sexual behavior that interfere with work, but doesn’t do a thing for irritability or touchiness, and may actually make that worse. Elevated progesterone mimics the hormonal profile during human PMS, too, and if you’ve ever been pregnant, you know you don’t exactly always feel positive and energized then either.
Regumate can cause temporary infertility, which will last for a while even after you stop administering it, so bear that in mind if you want to breed the mare. Mares coming off Regumate frequently have cycling abnormalities for many months. That can make them even worse than they were before they started the drug. Another drawback is that care must be taken not to get it on your own skin, where it can be absorbed and cause c[/I]ycling problems in women, or infertility in both men and women"
I have been told/heard using/trying Chastetree Berry works. I have never used it myself.
“If you really need something to control your mare’s seasons, a better first choice is often Chastetree Berry. Try a half-ounce to one ounce per day of the ground berries from a bulk herbal supplier like HerbalCom, www.herbalcom.com, or use an equine product like Hormonise from EquiNaturals, www.equinaturals.com, or Evitex from Emerald Valley, www.emeraldvalleybotanicals.com. This botanical is usually very successful in regulating cycles and toning down both behavior problems and irritability. Other mare supplements use different herbs, including many calming ingredients. These options are definitely worth trying”
This is good article on the subject;
https://aaep.org/horsehealth/estrus-suppression