110 amp battery will give you 1,320 watts of power = around 2.6hrs of use, however a battery stored in a freezing van will have its capacity reduced even more, so in affect giving you around 1.5/2hrs use through out the night with your timer.
Again as the battery drains towards the end of the night this again will reduce the out-put wattage of the battery to around 1/1.5hrs per evening, provided the battery was fully charged in the first place.
A very good idea you have in theroy but in practice its not practical, I would sooner see you spend your money on something better.
(This is without seeing the specs of the inverter that may reduce the batteries out-put even more)
EAOE
