I wonder how that will work for an 8 hour +/- duration? Don't kids toys with batteries usually turn off after x minutes, so how will it close the door after it opens? Plus the weight of the door has got to pull on the batteries if they are what is going to hold it open all day.
I'd hook up something to 110 house current, or at least a fully charged tractor/car battery.
You don't want them getting locked in the coop all day in this weather, or locked out all night if you fear they will be eaten.
The junkyard antenna and Goodwill powerpacks don't take much time to get and install. If you have power in your coop, or can run an extension cord from the house I would think that would be your safest bet.