Yes. If by some unlucky chance, a mare foals on Dec 31 or earlier, there’s a lot of scrambling to keep it under wraps for a day. Otherwise, for racing purposes, the foal becomes a yearling when it’s one day old.

This is an extremely rare occurrence except for the occasional premie though. Mares are bred to foal Feb - May in the Northern hemisphere, with occasional outliers in Jan or June. Horses foaled in May or June are usually not physically mature enough to race as two-year-olds, obviously, so you try for Feb and March foals.