If its plastic, it should be OK. If you insulate it, when it does freeze, it’ll take an age to defrost again!
If you are really worried, you can get a tape/wire that wraps around the pipe and gives off a little heat to stop the pipes freezing. Seems to start at about £6 on ebay for the dodgy Chinese/Korean stuff, £15 for something decent. They had it in the washrooms at a campsite, only noticed as the cold tap ran lukewarm for the first 20 seconds 🙂
PS Windchill doesn’t ‘exist’ if the object is already the same temperature as the wind, so won’t affect the freezing point. Unless of course, you have the above heat tape…then windchill would increase heat loss.