Answer: A horrible genetic disease found almost exclusively in Arabians. It's a recessive condition.
Affected foals are born normal, but within the first few weeks or months they lose brain cells. This leads to a tremor that affects only the head and ataxia - lack of balance. The affected horses move in an exaggerated manner, find it hard to get up if they lie down, startle easily and tend to fall.
They're often euthanized, because it's unsafe to ride or work them, and they tend to get hurt a lot. (Milder cases may be kept alive as pets - but in a world where horses are needed for work, it's rather likely that affected foals are going to end up, well, in the pot).
There's now a test for the gene that causes it. Thankfully.
Image source: Ealdgyth via Wikimedia Commons.