I'm having trouble picturing this

I was given The Charlemagne Pursuit by Steve Berry, and I've started it. So far (Chapter Six) it's all right. But I've just hit a sentence so bizarre it broke me out of the story and sent me here.

A colorful sleigh appeared, drawn by two prancing steeds, its riders tucked beneath plaid blankets, the driver snatching at the bridles.

First, a steed is generally a riding horse. Second, it's hard to prance in snow. Third, combining those, here's the kind of tourist sleigh you get in Garmisch-Parkenkirchen, where this scene is set. Those horses? Don't prance. And finally ... what the hell is the driver doing "snatching at the bridles"? And how is he doing it?