I know what you mean -- NOW -- after this winters heavy snowfall.
My 24" and 28" chickenwire fences were buried in snow. But when that happens, the raspberries are under the snow too.
I guess the critical time might be when only the upper 6"~8" of the fence is above the snow and the raspberry canes are exposed. I worried about that for my young fruit trees since I have plastic collars on them up to 18" of the trunk but with the snow up so high, the rabbits would've been able to reach the upper branches.
In my case, I had one medium sized blueberry bush caged in a hardware cloth -- a holdover from last summer to protect the berries from birds. The rabbits chewed off every bit of branch tips that grew out of the cage. I forgot to cage a small blueberry that didn't produce any berries last year. It has been THOROUGHLY "pruned" over the winter
You might just bite the bullet and build a complete cage around them because once you have fruits, you'll be fighting off the birds. And they'll take the berries just BEFORE you think they will be ripe enough to harvest.
I plan to build either a wooden or EMT structure and walk-through door completely covered with chickenwire. I've tried the bird netting for 3 years and am tired of squirrels, rabbits, and groundHOGS ripping holes for the catbirds to get in. I'm telling ya, they're in cahoots.