Sledog is right.
Cold temperatures don't "drain" a battery, per se. That is, they don't cause a loss of the stored chemical potential. What cold temps do is cause current flow to diminish.
So, you turn the key and not as many amps go to your starter motor. Further, your motor is cold, your oil is thick, and the turning resistance is high. All together, not enough compression/momentum is generated to start the car.
Solutions:
1. Allow battery to warm up naturally. At higher temps, it will provide more amps. If you have a charger you can put on it to make sure it is topped up, all the better. Obviously, if you've discharged the battery attempting to start the car, you will need to charge the battery (unless you jump, then the car will charge the battery after you get it running).
2. Remove battery, bring in house, warm up next to radiator or vent (charge if needed). CAUTION batteries can produce hydrogen gas, which is explosive, so ventilate and no open sparks. And don't put it in the microwave. When the battery is up to room temp, reinstall and you'll get more amps.
3. Jump - I try to avoid jumping. Jumping can cause problems. Further, in extremely cold weather, jumping is not as effective. You need to have heavy gauge jumper cables and a good car from which to jump.
4. Combine 2 and 3 if neither works.
5. Check battery terminals and clamps - should be shiny metal. If not, get a 3 dollar post cleaner (specifically made for this purpose) and clean the posts and clamps. You can lose a lot of amps because of bad connections, and I've had many connections get crappy in a year or less. You can use 100 grit or 150 grit sand paper to shine up the posts and clamps if need be.
A one year old battery should be fine. It would be very unusual to have a defective battery one year in.
Good luck. I guess I'm cheap. I wouldn't pay for a jump unless it was an emergency.
Oh, and is the battery sized right for the vehicle? CCA are the critical battery parameter. If you replaced an OEM battery with a battery that has too few CCAs, then you are going to be fighting this same issue again at some future date.
If your car is relatively new, and gasoline (not diesel!), then it absolutely should start down to single digits, no questions asked.
Jump packs and jumper cables are nice and all, but I'm a big fan of making sure you have a proper battery (more CCAs than OEM even!), good connections, and a young battery (replace at first sign of slowing crank rate). Do those things, and the main purpose of your cables and jump pack will be helping others out, which is good.