This is exactly what I did the first year, only I needed two hundred feet so I had to use 2 cords. Still with proper protection I never had a problem. Then we ran electricity out there, but I still use extension cords to bring it to the coops where and when needed. All connectors are inside an electrical box or inside the coop. It's safe. One time when I connected two inside the run in the snow to have electricity in a couple places, it burned out the connector. It did not draw enough electricity to start a fire, it just burned out. I wouldn't do that again, because those cords are expensive. That's why we ran electricity out there.Yes seriously! As long as your ends are protected and you use the proper stuff, it shouldn't be a problem.
I run a 12 gauge 100' extension cord to my coop. I have a covered power inlet on the side of my coop that the cord gets plugged into and the end from the house gets plugged into a covered GFCI outlet. I only use power in my coop for a couple months, when my water could freeze, so I saw no point in running permanent power to it.
If you don't want to do this and you have the time, the small dishes of water work pretty well. I change them 3-5 times a day with very warm water and they do pretty well. But then our temps only get down to 20's or rarely teens. So, maybe not an option for you. They love the warm water in the winter, btw.