We wired electricity to the goat shed (100 m from the house, it is thicker than the normal cables in the house, but I am not the DIY person in this house)with a short extension to the neighbouring hay/lambing shed and also now have a cable running out to the hen house from the goathouse (about 20m), just a standard plugged in cable). Just standard timer. works well.
But it seems the cold is just too much, eggs aplenty until the beginning of this week, now only 1 or so per day (from 13 hens). Cockerel also seems to be a lot quieter....