The engine turned over normally and started immediately, and the battery gauge showed the normal voltage, so I don't think it's the battery. In retrospect, I believe the steps have been like this for quite a few months (we bought the 24SS used 15 months ago). When we travel, the engine battery is charged almost every day; but in the winter, it's a month or more between uses, and then for only a 10-15 minute drive to warm it up and circulate the oil. So, the battery is cold, not fully charged, and the step gets less voltage.
It's still possible there is a problem in the wires from the step to the battery or ground, even if the battery is fin, as it seems to be. Still, I'd expect to see the full battery voltage when the step isn't moving, and not drawing any current, but I didn't.