I don't have an AT822, but use a similar kind of stereo mic (AT BP4025) which I find excellent for handheld use when out and about - City ambiance, etc. Typically, I use this with a Rycote BBG & fur, which is pretty effective for most situations. For the next step up in wind protection I have an original Rode Blimp. It works well in pretty extreme conditions and provides a much bigger airspace around the mic. The internal suspension also makes a difference. The Rode Blimp is quite a bit less expensive than the Rycote modular windshields, mainly because it's a "one size fits all" design. It comes with a variety of mic clips & there are no other options. I think the newer version uses the Rycote "lyre" suspension, which is an improvement over the rubber band arrangement used in my original.
If your signal is actually clipping from the wind bursts, the problem might be as much with your recorder input stage as the mic. One thing that I've noticed, moving from a Tascam DR100 mkIII to a Mixpre 6, is that the Mixpre's high-pass filter actually works to prevent much of the low-frequency overload. When I first got the recorder I was actually very surprised, since I'd assumed that it was the mic which was clipping! The Mixpre filter operates in the preamp stage of the recorder before the digital conversion and prevents the latter from clipping. I'm not sure about the Zoom F3 and a cursory internet search doesn't tell me much about its filtering. But this is something to bear in mind.
Of course, sometimes no amount of wind protection will help, but don't forget that getting close to the ground, standing in the lea of a large object, or using your body as a windshield, are all useful tactics. An ordinary fleece jacket thrown over the mic can be effective, too. The slight high frequency loss can be compensated for in post and anything is better than distortion!