Late winter winds can indeed be brutal. We use heavy duty plastic ties, and they work well. You don't want the ties to be TOO strong as the wind can actually take the fence down-you want the ties to break at some point, rather than the wind pulling the fence down. It's a pain to replace them, but really not all that time-consuming. We get pretty high winds and have elected this year to wait until about now to start putting up our outfield signs.
If we leave our screen up over the fall and winter next year, we may cut the bottom ties so it just blows up and flaps like a flag-much less stressful on the fence and screen.
Our screen also has cutouts, but we haven't seen where it helps much.