If you can I'd run the hose through the door and if needed put a wedge, or 5l container of water, behind the door to keep it shut if cold weather or security is a concern.
I have run hoses through upstairs windows plenty of times. Just be sure to use lots of dustsheets to protect the window edges, sills and radiators. I use an old climbing rope to lower and raise the hoses gently. A bit of pipe lagging round a QC will stop it whacking the glass.