Customer the possibilities of what could possibly be causing your problems are numerous. I will try to give you a list of items to check to help narrow it down.
The first thing I would check would be the PCM power and fuel pump relays, they are located in the fuse box under the hood. These were very common on the aerostars in the early ninieties. Turn the key on and look at the instrument cluster. The check engine light should come on. If the check engine light does not come on the PCM (The PCM is the engine computer) is not being powered up. If the check engine light does come on the PCM is powered. Second, turn the key on and listen carefully. You should hear a hum come from the rear of the van as the fuel pump primes it self. Cycle the key several times and listen for this. If you do not hear it, try switching the fuel pump relay, and try to start again. These two relays are the cause of more intermittant no starts than anything else on the early nineties Aerostars.
If those two things are ok, check to make sure the engine is not flooded for some reason. To do this, press your gas pedal all the way to the floor and try to start the truck. This turns off the fuel injectors to clear up any excess fuel in the cylinders that could cause a no start.
Next, check for good spark. Remove the plug wire from the center of the distributor cap and let it lay over the electrode on the cap. Try to start the engine and watch for good spark. If you have no or weak spark, you will need to look into the ignition system. A bad ignition coil could cause a no start when cold or wet outside. Also remove the cap and ensure the rotor spins when you turn the engine over. These engines had problems with the gear on the cam wearing and causing the distributor not to spin. Also, the ignition modules on the side of the distributor are known to go bad, usually they will not start when hot, or not at all though.
If you have good spark, find the fuel pressure test port on the fuel rail and depress the valve in it while cycling the key to see if the fuel pump is making enough fuel pressure to start.
These are the easiest things you can check on your own. You may want to have the trucks checked for codes with a scan tool. Shorted coolant and air temperature sensors can also cause the concerns you are having.
Hope this helps, if you have any further questions do not hesitate to ask.