Check the serpentine belt. You didn't say which engine you have but on most of them the same belt runs the power steering pump and the alternator. When the alternator isn't turning to keep the battery charged, system voltage will be low. The anti-lock brake system can't operate reliably with low voltage so the computer shuts the system down and turns that light on.

There is a splash shield available from the dealer to prevent snow from knocking the belt off.