Check your power at the battery, with a meter, not a test light. Also make sure the fuse at the battery isn't loose, or broken. Extreme cold weather tends to make parts shrink and break poor connections.

The power light on your amps and what not are turned on by the remote from the radio/head unit, Not constant battery power.

also make sure your ground to the amp is solid. You should see damn near zero ohms between a good solid non painted surface and the amps ground. A seat bolt is NOT the best place to ground your amp.

If all the power looks good, disconnect your subs and see what their resistance is. Between leads as well as ground. Depending how they are wired, I'd guess you'll see 2-8 ohms. Should be infinite ohms to ground.