Given the horsey theme (design and horsehair strings), it made me think of a Morin Khuur, the horse-head fiddle, the national instrument of Mongolia. But, that's typically 2-stringed, and all the pictures I've seen of it show a box-shaped body, not the round one. Maybe it's a related instrument from that region.

More info (and links) in this thread.

Here's another.

~ Becky in Tucson