While it may be the alternator, you might want to also check the build date of your van. My OEM battery (non ESS) was a 2 year battery and at about 28 months and 33,000 miles or so managed to throw some codes so the dealer checked the battery and it failed the test before it left me stranded. (They did replace the battery under the three year factory warranty somehow.)
I've seen failing batteries cause some mysterious electrical issues, but nothing quite like this. I've also seen batteries fail in only a few years; the battery in my Escape only made it three years. They can also last a long time, though...I just replaced the factory 12v battery in my 2006 Prius two months ago.
I'm not surprised that the extreme cold would be enough to finish off your battery. It will be interesting to see if your van's alternator has a problem. Why do you think it is the alternator vs just a dead battery? You actually got the red battery symbol. I've wondered where it was supposed to show up. I'm still trying to figure out that gauge and if it can help prevent a problem.
I'm fairly sure it's an alternator because of the symptoms. Over the years I've diagnosed and repaired at least a half-dozen alternators, and the symptoms were all like this. The car starts and runs fine, but the alternator doesn't make any power, which causes voltage to drop as the battery powers the car. After about a half-hour of running, the battery starts to fail and systems will shut down eventually leaving you dead in the water.
My van started up just fine, and ran well for over 100 miles yesterday on a few different trips. It was in the middle of a short trip across town that I got a "Charging System Failure" message and battery light. I scroll to the battery voltage and see what I posted above, which indicates the alternator wasn't making power. I drive right to the dealer, shut it off in the bay. It started perfectly fine at least twice more as they moved it up in the bay, then out to their lot after checking in, all the while with the warning light and message displayed.
Contrary to popular belief, cold weather doesn't kill batteries. Up here it's not uncommon for batteries to last 7-10 years or more, just like the one in my Prius. Cold will certainly reveal a weak battery, though.