First off, you should most definitely put a new battery in it, if you are still on the original. You did very well to have it last this long for you.I read some postings regarding this issue. Is there any association between warming up the vehicle before driving it during cold weather and this magnificent light?
I had an experience with my 2010 Honda Pilot last night. It just suddenly died. It would not start after pumping gas. Road service brought back to life. However, this morning I notice this light VTM-4 came on.
This afternoon on my way home the light failed to come on. I am confused. Is it the battery (it has the original).
Second, the VTM-4 light comes on for a multitude of reasons. You need to find out if you have any diagnostic codes (which you should if your check engine light came on). Then go from there. Hopefully nothing major going on. I've heard of a lot of mysterious things happen with low batteries, but nothing like you've described; but who knows.... if the Engine's computer decides to act weird due to low battery, all bets are off. Find out what happens when you infuse some fresh juice!
While you're at it, another easy thing you can/should do is to look at your oil & radiator fluids. Make sure they look good w/o contamination (milky, etc.). If you are REALLY unlucky, you could be looking at a more significant issue like a head gasket or cracked head.
But the cold thing you mentioned supports the "battery" suspicion.