What is the name of a fancy headdress for horse?

There isn't really a single name for a "fancy headdress for horses." The specific name would depend on the style and purpose of the headdress. Here are some options:

For Show/Performance:

* Bridle with a browband: These can be adorned with jewels, feathers, or other decorative elements.

* Fancy headstall: Similar to a bridle but without the bit. Often used for show or costume purposes.

* Costume headpiece: These can be very elaborate and designed for specific events like Halloween or a horse show theme.

Traditional:

* Shabraque: A decorative saddle cloth that can be elaborately embroidered and often features a headpiece.

* Native American headdress: Many Native American tribes have traditional headdresses for horses, often made with feathers and beadwork.

Other:

* Floral head wreath: Can be made with real or artificial flowers and used for events like weddings or photo shoots.

* Diadem: A jeweled headband that can be used for special occasions.

To give you a more specific answer, I need more details about the style and purpose of the headdress you're looking for.