Running an extension cord across the yard to the coop is maybe something you can get away with (most of the time) if you HAVE to, but is really not especially safe and it would be a real good idea to take steps as soon as possible to NOT have to do it.
If you DO run an extension cord, it will need to be from a garage or outdoors receptacle (preferably one of the ones with the lid that can be closed fully even when a cord is plugged in), it should be a HEAVY DUTY extension cord (yeah, even if you're just going to run a waterer heater and a light), and run it somewhere at or near ground level (not up on a fence) that's out of the way of tripping, lawnmowers, and rodent nests.
It would be a whole lot better, though, to get an actual electric line run out there as soon as possible - buried conduit, GFCI, and preferably its own breaker.
Good luck,
Pat