Hi
My RO usually works all night so when it is, it isn't a worry.
When it not working, ie. weekend, then I uncouple it from the outside tap and put it in the bath before we go to bed. Always put the bath mat in first so any dirt on the RO won't scratch the bath's surface.
The wife hates it but hey, it works for me - although I can't say we had too many freezing nights last winter in Saltburn, Cleveland.
Rgds
Spruce