I have a 2001 malibu , my cars engine light has been for about a week. This is the second time it has happened. lately I have been having trouble starting my car. Does this have anything to do with my car , or because of the cold weather? How important is it for me to get my car checked out?
You need to at least get the car checked for codes. The chain type auto parts houses will do this for you free. Whether the CEL has anything to do with the hard starting is unknown at this point.
The job of the parts house is to provide a code; not diagnose a problem. You might post back with any results.
When my wife or kids have asked a question about a CEL, and with tongue in cheek, I tell them not to worry unless it’s PO666, the Explosion Imminent code… 
Get the car checked out. The engine light is on because something is wrong. The hard starting is because something is wrong. A car is good shape will start right up even in cold weather.