Charming carved horse head handle! I believe it is for a parasol or umbrella. It appears to be some sort of plastic, possibly end of day bakelite as it has very thin lines of blue, red, purple, and green in its mane. The rest is shades of brown. I tested it with Simichrome cream, and it was inconclusive.
The horse's head is thin and has elegant lines, really a lovely piece.
It is in excellent condition and measures 3.5 inches across.