We have a lot of wind too. I tie my chair pillows to the chair frames. Some I purchased had the ties on them, so for the rest I added a piece of cord or rolled material to use for a tie. I did tack them on with a needle and thread.
You can get velcro strips to secure it to the chair frame
Can you use outdoor velcro?
There is no 'outdoor' or 'indoor' velcro.
The difference may be in quality of brand name vrs no name, or in the thickness or density, not in the function.
This is a really great idea for securing outdoor pillows: https://www.youtube.com/watch?v=3Rtx21EHBEI