When you say "the warnings flashed again" after replacing the battery, are you sure that it was the same warnings that occurred with the previous battery or possibly different warnings? The reason that I asking is because of a very possible scenario:
- Your 12V battery as you suspect was done. Normally however this would only affect starting the car, but in some cases a really far gone 12V battery will cause warning messages to appear while driving. Somewhat unheard of however is for a bad 12V battery to cause the car to die once it is running, but it might be possible.
- After replacing any 12V battery in the Clarity, or even disconnecting a healthy battery for a few seconds, it is perfectly normal for the instrument panel to display several ominous warning messages about failures of VSA, ABS, TPMS and I think one other. Yes that is perfectly normal to see those type of warning messages anytime the 12V battery is disconnected. These messages clear in less than a mile of driving.
If it's not those messages, or whatever messages you are getting don't go away within one mile, then there would likely be something else wrong with the car. But without further details about what error messages you have been seeing I am leaning towards it being the scenario that I described. I.e. just a 12V battery that went bad, as you surmised likely due to the sub-freezing temperatures, and then the normal "boo" that the Clarity does whenever the battery is replaced or the 12V is disconnected.