Car will not start in damp or cold weather

The most common suspect is the pickup coil inside the distributor, but there are two versions. One system uses just one pickup coil. There will be a single connector with two terminals at the end of about six inches of wire. The other system uses two of those pickup coils, one for cranking and one for running after the engine starts. That distributor will have two 2-terminal connectors. Those coils are identical, but they are positioned slightly differently so the "crank" coil retards ignition timing a little so the engine will start easier.

When you have two pickup coils, switching between them is done with a relay. That relay is another good suspect. A quick test to check for a defective pickup coil is to just unplug both of them, then switch the connections. You will be cranking the engine on the "run" pickup coil, which has more timing advance built in, so the engine might crank with slightly more difficulty, but if the "crank" coil is bad, the engine will run on that "run" coil until you release the ignition switch from the "crank" position, then it will stall.

If you have the small five-terminal ignition module, (only uses four of them), on the inner fender, the housing is the ground connection. Be sure it is mounted solidly to the body and those bolt holes are not rusty.