Andy didn't say this, but he has a CTLSi, with a Lithium battery rather than the Odyssey. I don't think it would hurt to plug the battery charger in when you plug in the Tanis, but I am not sure about keeping it plugged in all the time. With as cold as it was I doubt the Tanis provided enough heat to warm the battery much. One thing that might help to warm the battery would be a cowling cover to try and retain the heat in the cowling.
I pulled this from the Shorai FAQ page.
A. Down to about 20 degrees Fahrenheit (-7C) most users find that they can start normally on first crank. If your headlight comes on at key-ON, it is good for the batteries to flow some current before cranking in cold weather. The suggested headlight-on time before cranking depends on the temperature. If starting at 40F/5C, 30 seconds will help wake the battery and increase cranking performance. If at 0F/-17C, leave the lights on for 4~5 minutes before cranking. The result will be a better first crank, and longer battery life. If the engine fails to start on first crank, that first crank has warmed the battery, and the second attempt will be much stronger. Other accessories that can be turned on before cranking can also be used for this purpose, such as heated gear, radio, etc... Insuring that the battery is fully charged after storage also improves first-start performance in cold weather.