Baz is right. If you're going to buy batteries specially, get 'deep cycle' marine / campervan type ones. These are designed to be charged and discharged, and will therefore last much longer. They'll also be better for using with your electric fence in the summer.
My solution last year was a 240V submersible aquarium heater, like the one below, stuck into a bucket of water:
This was very cheap, and worked very well (a bit too well actually, and I had to run it on a timer for 15 minutes out of every hour, or the water got warm). Is 240V definitely out of the question for you Suzie? Alternatively, I wonder if you can get 12V versions?