90 Tercel will not start in really cold weather

Clicking could be the ignition and fuel pump relay-

Next time it refuses to start don't wait for it to make up its mind-do below immediately to determine if its fuel or spark problem

Get a helper disconnect a sparkplug wire or 2 and ground it to the engine atleast 3/16 away from ground-have helper crank engine over-do you have a snapping blue spark? If so-you have a fuel related problem, Do you hear the fuel pump come On when you turn key on? If not check fuel pump fuse and fuel pump relay if so, check the fuel pressure to rule out the fuel filter/fuel pump/pressure regulator and listen to the injector/s are they pulsing or hook up a noid light. No snapping blue spark continue to troubleshoot the ignition system-power input to the coil/coil packs, coil's resistances, cap and rotor, distributor pick-up coil, ignition control module, cam and crank sensors and computer Note: If it doesn't apply disregard it and keep testing