As an ex-Rochestarian I can tell you your car just doesn't like being frigidly cold and covered in snow and is letting you know  Really don't have any knowldege to add, but if your battery went dead you'd lose the keep alive - so if for some reason the mixture or idle settings had crept way out at max over the last 100k miles to keep the car running it's forseeable that it'd have trouble starting after losing the memory. However - if you aren't hearing the fuel pump trip and you don't see the check engine light come on with the key to run position you're probably right in looking at the PCM. The pump is much easier to hear with the back seat removed btw.
97 Contour SE MTX
K&N 3530, UR UDP, 19# Injectors, mystery mod, FMS wires, Fordchip.com chip, SVT: TB, Flywheel, clutch, exhaust
04 Grand Caravan SXT
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