problem from the cold?

its possible you have several small unconnected problems
stalling could be do to
1 cold weather
2 oxygenated fuel (they add alcohol in the winter)
3 dirty sticking choke

battery problem could be
1 bad battery ( I have had brand new ones go bad in a few months)
2 bad connections sometimes they look fine but are not, take the wires off the battery terminals and really clean them well with a wire brush then put them back on tight
3 battery could just be low from not driving enough, it can take up to 15 or 20 minutes of driving to recharge the battery after each time you start it up, put it on a charger until its fully charged

bad charging system
1 check alternator and regulator
2 check for loose or dirty connections