Hmm, I have never thought about it that way but, I can see your logic if the neighbor(s) knows nothing about overwintering or plants in general. Although I am not sure why "it looked bad". In my version of it, leaves are piled around the chicken wire so all I saw was the leaves on top of the cardboard... so nothing much to "see".

Personally, knowing the reason why you are doing it and knowing what it does to the hydrangeas, I would suggest that you do not be concerned what anyone else thinks. Or be embarrassed by.

My first attempt using chicken wire was a pain and odd looking but no one ever said a word. Give the neighbors some hydrangeas to take care of in their own gardens and then guess who they will be called for help all the time! Ha!

Additional, similar methods that you can use also include using chicken wire or burlap.