You can have the hook permanently tied up in a tree with a piece of string, then you can poke the sharp end through the netting and slide it along. Makes it quick and easy to remove and replace the balls and you don't have to fumble with frozen fingers for too long.
I haven't had an opportunity yet to test that this material can tolerate temperatures below freezing but there is no lower limit mentioned in the Shapeways materials guide. Only an upper limit of 80 degrees Celsius.
Update: The hook has been hanging all winter and is just the same, so frost is not a problem.