I have an '87 Plymouth Voyager that won't start when it's cold and/or raining outside. Any thoughts??

Several, first if your engine has a distributer then replace the distributer cap and wires it is drawing moisture and not allowing the car to fire. Second, if you have a distributerless ignition then remove the plug wires and coat the boots with dielectric grease. This will help keep the water out of the coil and should allow it to fire better. Also coat the inside of the spark plug boot with the same material. Finally, make sure that the wires to the ignition are clean and dry that should allow for good power flow the ignition system to insure good starting.