Yes, the prefab coop manufacturers grossly overestimate the population capacity of the coops...unless you want to keep your birds in factory farm type spacing, most of us here do not want to do that. It's a rude and heartbreaking awakening that many newbie chickeneers are faced with. You are...
14ga 2x4 welded wire over the chicken wire would help....14ga 1x2 welded wire wire would be even better.
Keeping the snow off it may be tricky, will need supports underneath and a roof rake to scrape off the outside what can't be banged lose from underneath.
As you may have been told in your other two threads,
https://www.backyardchickens.com/threads/lost-half-my-flock.1322014/
https://www.backyardchickens.com/threads/help-hlp-can-i-create-a-fortress.1322107/
chicken wire is not predator proof, except against hawks, raccoons can chew thru it...