My V6 SOHC (1999) with a recently rebuilt transmission often dies when I pop it into reverse
right after a cold start. It gets much worse in the winter, sometimes it dies when I pop it into drive following a cold start. Turning the steering wheel after a cold start sometimes also causes the engine to stall... in other words, any load applied to it *sometimes* causes the engine to stall and die. However, these occurrences are pretty rare and he truck works as it should the rest of the time... I'd say it only happens once a month and only when certain conditions are met. Also, you can feel it stalling a few seconds before it actually dies on you and giving it a little gas when it's about to die usually helps... just make sure you're not going to run anyone/anything over when you do it!
That said, the problem used to much worse many years ago (when I fist bought this truck used), but replacing the IAC valve (a common problem on these) helped greatly - I actually found that info on these forums and it solved a major issue for me back then. The valve assembly is a breeze to change, as it sits right on top of the engine under the big plastic cover. The cost at the dealer was around $100 approx. 6 years ago, but since you're in the good'ole US of A, your prices are probably much better (we get f*cked over on everything up in the "Great White North", aka Canada).
Now the good news (I guess, lol)... my truck has been doing that periodically for as long as I've had it and I consider it as "normal"... as in nothing to be concerned about. And yes, if it dies, cranking it up will start it up again right away. I don't remember it ever having this problem in the summer, it only tends to show itself on cold and/or damp days (rain, snow, etc).
Anyway, I still love my Explorer even though it has it's moods sometimes... I consider it as being it's "character" and not really a defect. Every vehicle has it's little special gremlin here or there and the 2nd generation Explorer is no different.
P.S. My truck has had a complete tune up done not too many miles ago (less than 30,000)... fuel filter, air filter every year, spark plugs, plug wires, IAC valve (mentioned above), injector cleaner poured in tank every few few fill ups, etc. The problem was diminished after these things were performed initially, but definitely hasn't disappeared completely. I think it has something to do with the way the PCM addresses engine load in idle... as in not enough engine RPMs to support the full load in idle or poor PCM responsiveness under load, which would be a design flaw. Anyway, it's not a big issue to me.