The Adelphi Hotel is legendary in town, but unfortunately it closes down at the end of October. Apparently, it cannot be heated appropriately and so they close after racing season ends.
Race Season was over, but I still saw the famous track.
And the museum is open year-round:
They had A LOT of horse statues in the museum. I can't tell one horse from another, really, especially when they are immortalized in bronze, but you're allowed to photograph Secretariat.