You should store the battery in your garage not in your house. A charged battery will not freeze. Cars sit outside all the time in the winter with well below freezing temps and below zero degrees. Don't worry about that. I would leave it in the garage and charge it overnight on the 2 amp setting or longer until it shows full charge once a month. That is all you need to do and you will be ok but don't store it in your house.
Glad you got both your cars batteries clean up.