There are a few possibilities;
If the battery is the origanal or old the cold weather may have kept it from turning the motor over fast enough. It takes full power on a cold day to start a motor.
You could have an ignition system of fuel system amanagent or delivery issue.
You can check the fuel pressure by getting a test kit, both Advance Auto and Auto Zone loan them out with adapters for the test port on the fuel rail, and turn the key to the, "ON" or "SART" position. The pump should prime the system and you will be able to see it on the gauge. It should be anywhere from 35 to 45PSI roughly, if you do the test and need the exact spec just ask me and I will get it for you.
There is a part that works like a choke on fuel injected engines which is eithre a Fast Idle Thermo valve, FIT, or an Idle Air Control Valve, IACV. you probably only have the IACV. It is located on the intake manifold near the throttle body and has either an electrical connector or a vacuum line running to it and may have coolant lines running through it. It may have failed or is failing.
I am giving you a link to a walk through diagnostic that will cover all these areas and some others in depth. It is a good diagnostic tool as you can reference it and it has video and pictures to help you identify the part you are looking for.
Here is the link;
Friday, March 17th, 2017 AT 1:09 PM