What is a partially tamed horse called?

There isn't a specific term for a partially tamed horse. However, depending on the context, you could use terms like:

* "Untrained": This implies the horse is not yet fully trained in basic commands and riding.

* "Semi-tame": This implies the horse is starting to trust humans and is manageable but not fully trained.

* "Green": This term is often used for young horses that are still learning the basics.

* "Breaking in": This implies that the horse is currently in the process of being tamed and trained.

The most appropriate term will depend on the specific level of tameness and training the horse has achieved.