Check out the examples on Merriam-Webster; they have one for scary meaning frightened that matches my own experience.
I actually came to this all ready to explain how it's a rare usage, and I still think it is, but M-W are all on top of that.
However, I disagree with their actual definition for that usage. But let's look at it:
a scary horse who spooked and kicked at its own shadow
When a horse is prone to getting frightened, either in general or as a temporary mood, we use words that sound like they mean something else in other contexts. To indicate that it's easily scared, we say it's scary; to indicate that it's easily spooked (almost the same thing), we say it's spooky. The horse community has a lot of words that are recognisably unique to that domain, but they also have plenty of words that have subtly (or not-so-subtly) different meanings from their general use.
For instance, both the verb to spook and the verb to scare can take both their usual meaning with respect to horses, and a slightly alternate meaning. If a horse spooks, it means a fairly specific set of behaviour and movement, where it stops and jerks backwards and/or sideways, maybe rearing a bit. If you spook a horse, then properly, you've caused it to spook. It's a little less common (possibly a little archaic), but the same applies to a horse scaring. When a horse scares, it is frightened, but more specifically it might spook a bit (or it might not), and then it runs off with disregard for instructions from a human - even a human on its back. Assuming the human on its back has managed to stay on its back.
Thus, a horse that is spooky is prone to spooking or close to spooking, and a horse that is scary is prone to scaring or close to scaring. For a horse to be close to scaring, it's probably already a little out of its wits with fear (or sometimes other causes - drugs, agitation, irritation by insects, etc.).
That sense of scare seems to have been overtaken in recent decades by the similar (but not identical) term bolt. However, I've never heard of a horse being bolty. The scare usage turns up in phrases that are slightly more current, like "horse scare", referring to an event where one or more horses scared and it became somehow notable. I suspect it's also the origin of such uses as "he doesn't scare easy", meaning that it is not easy to frighten him; I believe that expression was originally specifically used for horses (and other animals), got ported across to humans, and lost its distinct meaning of scary. Similarly, the saying "don't scare the horses" most likely didn't mean "don't make the horses frightened", but "don't cause the horses to run away in shock/agitation". Now it is used metaphorically.