Starting last winter my car stalled on me several times when I start driving before the car is heated up. It went away in the spring when the weather heated up but last night my car stalled again after i drove it right after starting it on a cold night. What could this problem be?

It only started last year and I also noticed that when I'm at a stop light or in traffic when the car is idling it kind of makes this coughing noise. Quiet idle for 10-15 second then it'll make a puttering/coughing sound for a couple of second then repeats every 5-15 seconds. It's kind of annoying since the whole car kinds of shake; not as bad as some i've seen but it's enough to annoy me.

Let me know if you guys know what could be wrong.

 

Worn spark plugs could possibly do that. Have you ever changed plugs? How many miles on the plugs right now?

 

How many miles on it? There are several threads on stalling when cold and most of those problems solved by getting your valve clearances adjusted. Search for the thread "stalling when cold."