Is there a cordless snow blower?

yes it's gasoline powered, haha, no battery ones I've seen, even the gas electric start models use house current to start

Actually Ariens makes a battery powered snow blower, I just saw it on their website. I have not seen one for sale. Call your local Ariens dealer

you are right, i found a review on the machine. it will cost around 1500 dollars, will run 45-60 minutes, and require 7 hrs for recharge, for another few hundred a 2-3 hour quick charger is available.