As a resident of Northeast Wisconsin, I may have a few suggestions.
1st- Buy a good sturdy netting. Woven netting is cheap but I found that racoons can rip through this very easily. I would suggest knotted netting over woven.
2nd- Determine what size netting that you need. 2" knotted netting will allow more rain and snow to fall through without accumulating and weighing down the top net. Although you might think that this would be my choice, I opted for the 1" netting because of the predatory owls that spook my birds and cause them to fly. The birds get their heads caught in the 2" netting which gives the owls a free partial lunch or they just hang themselves.
My coop has supports every 10 square feet to keep the weight of the snow from tearing the top net. Posts with and old hub cap nailed on top keeps it suspended and free to move if snow builds up in one area more than another. Don't ever secure your netting other than around the perimeter of your coop or run. Let the top be free to take up any weight on top or possible bird flying up into it.
The only time that I have problems with my netting is when we have heavy wet snow. With the supports, I am able to go into the coop and bump the netting until the snow falls through.
Not really sure if Oklahoma gets as much snow as I do but you can use my example as a "most extreme" situation.
I always like to be one step ahead of weather and predators. A few extra dollars spent to ensure the safety of your birds is less than the cost of losing them and replacing the cheap stuff with what you really need. LOL. I found this out the hard way. I hope that you don't need to.