It's less than a minute after she's out the door that the Doctor's after her. Thankfully, he's got that Time Lord toughness to help him along, but it's still bloody cold, and all he's had time to throw on was a poncho, with another one grabbed up to wrap around Amy once he finds her. He's tracking her partly by the tracks she leaves, and partly with the sonic, although with the blizzard, even that's not exactly doing a perfect job of pinpointing her.
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"Amelia? Amelia!"