You should be running lighter weight oil in the motor anyway, which should make it easier to crank over. Stock batteries are usually sized with enough reserve capacity so they'll still start the car when the motor is in bad shape.
The stock battery in my car is rated at 640 CCA and it weighed 42 pounds. I replaced it with a 520 CCA battery that weights 28 pounds. The terminals are the same top mount, no special adapters, and it handles frequent restarts just fine.
Others in the DSM world have reported being able to drive normally with a 320 CCA battery from a riding mower.
My other car has a 13 pound racing battery. It needed special hardware to attach the wires and a smaller mounting box and strap, which also saved a little bit of weight. It all cost about $100 Check out www.Stealth316.com/2-dynabatt.htm for more info.
Some other members on this site have gone the other direction with their batteries. A bigger battery lets you drive without an alternator which reduces parasitic drag. It also opens up the possibility of driving long distances without an alternator as long as you plug it into a trickle charger overnight.
at -0- degrees F. your engine is twice as hard to turn over, and your battery only has 40% of the power that it had at 80 degrees, and according to the Auto Refernce Book, at -0- your engine is twice as hard to turn over as well.