A horse that is in training is a horse that is being trained.
This horse may or may not be in good condition. Chances are that the horse is in good condition because he is in training. He will be given the best diet, follow the best exercise routine, and have the most attentive medical care.
We say that athletes are in training, too. At the beginning of, for example, the baseball season, the players may not be in very good condition. In their free months, they may have eaten too much rich food and drunk beer and not exercised properly. The goal of their being in training is to get them back into top shape as quickly as possible.