I own a 1991 Honda Civic that will not start in cold weather. During the problem I was able to remove a spark plug wire and there was no spark. Then it started up and it hasn't happened again since.
Checking for a spark was a good place to begin, and there was a recall involving the igniter on certain Honda vehicles.
The igniter is the term Honda uses for the ignition control module used on its electronic ignition systems. Honda recalled a very large number of vehicles due to a batch of defective igniters that were leaving drivers dead in the water. Your Civic was one of the vehicles involved.
The first thing to do is pull the distributer cap off to see if the igniter was replaced with the new design. The igniter is the unit bolted to the distributer base with all the wires attached. If it's black and embossed with the letters OKI, then it is the recalled unit and needs to be replaced.
If it is brown and reads NEC then it has already been replaced, but be sure all the electrical terminals are secure. Honda will replace the old style igniter regardless of the age or mileage.
After ruling out the recall it's gonna require a schematic, an electronic multi-meter and a little expertise to accurately diagnose the problem, but I can give you a couple of hints. No start cold is a common symptom of a bad ignition coil, and Hondas have always been tough on distributer rotors.