The ICE is kicking on more because it's cold and the Prius is keeping the catalytic converter up to temperature. The 12V battery is charged at a 1.4 amp rate though the inverter when the Prius is in READY mode, so it's not going to affect how often the ICE runs.
At 12.15V, it's time for a new 12V battery. Some people replace the OE battery with a Optima Yellow Top or Odyssey battery. These are deep discharge batteries that can withstand many total drains. They require a kit to mate the terminals to the Prius because the Prius uses JAL standard connectors. They also require padding in the battery holder because the physical size is different.
The 0E 12V battery on the 2001 was just replaced a few months ago. The 2004 hasn't had it's 12V battery replaced yet. However, in colder climates, automotive batteries don't last as long.
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