I am in Minneapolis - lots of snow - and use 2 inch square netting -
https://www.ebay.com/itm/Netting-Poultry-Plant-Bird-Aviary-Fruit-Garden-Protection-Net-Nets-Long-Lasting/312003119558?ssPageName=STRK:MEBIDX:IT&_trksid=p2057872.m2749.l2649
My run is 12 feet by 27 feet....I spanned aviation wire atop the perimeter and at three foot intervals across, tightened with turnbuckles....attach the netting with hog rings and you have something that will not sag and looks quite nice.
Last winter there was only one snowfall - heavy and wet - that really collected on the netting.
Knocking it down with a broom was quite easy. TWO inch netting - ONE inch might produce different results.
If you do have snow, I would advise against chicken wire on the top....I have heard too many stories of it all collapsing after snow accumulation....google for pics...there are many.