Yes, for horses one product you can easily find information on is called Regumate.
Horse birth control.
I've never administered it for "breeding" reasons...
I have administered the product to many performance mares to stop them cycling....
Their cycling made them crampy, sore and miserable so for a consistent performing horse, in this case these were champion reining show horses...the product alleviated much of their symptoms.
It is costly to have a horse, any horse on drugs for maintenance issues....menstrual cramps and such fall under maintenance = $$$$.
For a beginner rider/owner to purchase a horse knowingly needing this kind of maintenance to me is ridiculous.
There are many very beginner friendly horses available in all riding disciplines if you just take the time to look.
Mare or gelding...each animal is a individual and should be evaluated as a potential riding partner based on their knowledge, patience, personality and how they work with that rider.
There are no true set rules that mare is ___, gelding is ___.
People make comments like this that are not always accurate and sadly can sway a non-informed person into missing the horse of a lifetime because it was a ___.
True horseman/woman know that every animal should be judged on suitability based on the needs of rider and horse matching well, getting along, working together in harmony...regardless of beginner or very advanced capabilities...if not a team approach it just doesn't work well.
Hope that helps some. Limiting your questions like you just did to a refined area allows for better answers and comment pertinent, not just all over the huge spectrum of "horse".