"Breedy" is a colloquial expression that makes an adjective out of the verb "breed." Hence, it means the horse easily produces offspring. Other synonyms include:
Fertile, fecund, prolific, sexually productive, etc.

In Japanese, I came up with:
子孫が授かりやすい
多産系である
出産能力が高い
元気
繁殖力が高い
などなど

Good luck.