When you park the car before your trip, remember to park it so that you can get to the battery to jump start it if needed (usually, that means backing into the parking space). Also turn off all your accessories (radio, lights, heater/defrost blower, rear window defroster, etc). Although some cars de-activate these as the car is being cranked, you don't want to take the chance--you want all available juice flowing to the starter.
I've got one of those small solar battery trickle-chargers. I don't know if it makes any difference, but I haven't needed a jump start since I got it.
Be sure your car has the right weight oil for the winter. Many new cars recommend 5W-30 year-round now, but some manufacturers recommend thicker oil in the summer, thinner in the winter. If you've got oil that's too thick in the winter the car will be a little harder to start, and it also won't be good for your engine.
No car cover or engine blanket is going to keep your car any warmer for a 10 day period, unless it has a plug on it.
You should be fine. The battery is new, the weather isn't that cold, and 10 days is not an extremely long time.