It shows up more in colder temperatures. Like you've said the fluid can move quicker. The fluid will warm up faster, the seals warm up faster. The colder these old seals are, the harder and less pliable they are, so they don't conform to the retainers as well.
Your trans is fully electrically controlled by a module. Its located on the firewall next to the two relays, over towards the right side. There should be a code set for this, a code 35, loss of prime. Its a strictly hydraulic code.
Your trans is fully electrically controlled, the module controls solenoids on the front of the trans, this applies most of the clutches. If there were an electrical problem with a solenoid, pressure switch, or a speed sensor, the controller picks this up and puts you in limp in. To do this it shuts off the relay that powers the shift solenoids. Some solenoids are normally applied, some normally vented. This means when they are turned off some of them will apply clutches, and some of them won't. When the relay is turned off to give you limp in, the low/reverse and 2/4 clutches both come on, normally applied soleniods. This locks you in second gear only.
So, there will probably be a loss of prime code, possibly codes that have to do with individual clutch circuits having loss of prime because the pressure switches aren't closing, but a true electrical problem will lock you in second gear and turn the engine light on.
Since you mentioned the age of the module, I will too! There have been many hardware and software improvements to the trans controllers over the years. If you do have the trans rebuilt, you might think about replacing the module too. You'll notice a difference in how nice its shifts with the newer software. I recently went through this on my own 1994 Intrepid. The transmissions and controllers are almost identical, I spent the extra $175 or so on a new controller when I was done.