If it is fairly calm, and depending on the direction the wind is blowing, walking can be all right ... little bit gusty but not too bad. But the first time we walked it after moving here, it was quite windy, and that is a challenge. The wind just takes the breath right out of you, and it is tough going. Fortunately the railings are high ... above my head ... so we won't likely be blown off the bridge.
As for cycling ... I've tried to cycle it several times, but have only successfully managed to stay on the bicycle for one crossing, in one direction. Every other time, I've been off and walking soon after starting to ride ... just too gusty for me. Rowan can make it across, but he's got a lot more upper body strength.
And last weekend, we were planning to cycle it (or attempt to, in my case), but the wind was gusting up to 100 km/h (again), and so we opted to put the bicycles in the van and drive across. Just a bit too scary to cycle or walk in those winds.