How cold does it actually get there? It's likely they will not need the heater. I would not recommend a heater in that coop - it's much too small and the chickens wouldn't be able to get out of the heat if they wanted to. They may also not acclimate well to the cold with a heater on them all night so may not be able to tolerate being outside during the winter which they need, especially with a coop that small.
Also, the heated waterer must be placed outdoors or in an area with ample ventilation because they create a lot of steam that will collect on the walls, ceiling, and your chickens' combs and wattles and freeze.
Do you get snow? If so, raise the extension cord off the ground. I attached mine to fence posts with removable plant ties.