Back when I had an electric stove, I couldn't get water to boil for a pound of pasta, let alone 6.5 gallons of anything. That may have been an especially crappy stove, though.
Some of my old pots still have the spiral imprint from the heating element, too. I'd be willing to bet that you'd never get a good boil, and would over-caramelize/burn the wort.
I live in San Diego and brew in the garage with the big door open, so I know all about brewing in cold weather... it gets all the way down into the 50s here some nights! There have been some nights in January or February where I couldn't even wear flip-flops while brewing. Crazy, I know.