When you say "car will not start" as in, it will not turn over or crank - or more like, it will crank just fine - just doesn't fire?
First make sure that the battery terminals are making a good connection - shouldn't have any corrosion or loose wores/clamps there. Then I would have done is to have the battery checked out - you can take it to most Autoparts stores to be tested for free (usually takes about an hour or so - most places will charge the battery first and see what happens when they load it down). If you can eliminate the battery as the cause of the starting issue - then look to ways to improve cold weather starting. Running the right viscosity of motor oil (a full synthetic oil can make a huge difference in cold weather starting), making sure that the engine is in good shape, look for broken wires, loose connections, etc. (example would be the ECT sensor - if the coolant sensor reads incorrectly, can cause very hard starting).
But since you indicated that the car starts fine when jumped or during warmer weather - my money will be on the battery being bad or a bad connection from the battery. I've actually been stranded once by my Matrix - battery was about 3 years old, car driven often enough on (mostly highway) to ensure a good charge. Ran perfect one minute, then flat out died. The OEM battery is a poor excuse for a battery - you can easily pick up a bettery battery for about the same price as OEM with usually much more CCA and reserve capacity. Hard part is finding a decent fit for the vehicle.