You can definitely tell something is going on when the active noise canceling is on but it's not a big deal most of the time. It's good at blocking repetitive noise (office, car, plane) but bad at blocking other things like a car horn, a gun, someone clapping, &c.
Depends on how they're set up. My Sony over-ear noise-cancelling set has ambient noise mics that assume a non-windy environment, and thus can pick up wind noise themselves. I turn the noise-cancelling off if I'm going to be somewhere windy, but I have a hunch that putting a little faux fur patch (deadcat) over the ambient noise mic port would fix this.