Not as long as you don't seriously overdo it, especially not the NTG-3 which can take quite a beating. What you will get if blowing too hard into a regular microphone is an absolutely useless distorted sound though, and any directional mic will get boomy as hell from any kind of wind. If you wanna use actual blowing noises, an omnidirectional mic is a much better choice.
Ribbon-mics can get trashed by just sneezing into it, they're extremely delicate, but both dynamic, electret and condenser microphones are pretty solid in that department.
There are numerous ways to record wind as well as designing it, myself I've used everything from hanging the mic from a car at decent speed and covered well in windshieldings, to rubbing canvas to miking up a drafty window to actually using a noise-generator (both my JUNO-60 and the POLYSIX can get decent stuff, and to some extent my C-64-synth and the SQ-80, although they're much more limited in application). Though synthesizer sounds never works for anything but pure sweetening (adding elements to enhance rather than actually lead anything).
Here's another post discussing the subject:
Creating Evocative Wind Sounds