You can leave the Zero-G hose outside if it is not in use, but make sure it is clean. Cleaning is the most important part of a Zero-G hose. If you are planning on leaving it outside, make sure you clean it out thoroughly after each use. You should also make sure that it is not frozen before leaving it outside.
Clean the hose by removing it from the water tank and run it under a tap until all of the water has been removed from it. Remove any dirt or grime that may have accumulated on the inside of the hose and reattach it to the water tank.
You will need to remove the cap on the water tank and remove the hose so you can clean it. If you have pets, make sure that they do not chew on the hose.