Adjusting cookie recipes for high altitude
There is a fairly detailed answer to this available here.

It appears that the answer depends a little on the type of cookie.  If you have a cookie that has a great deal of air in it you'll have the same problem as cakes do.  If you are working with a very dense cookie that can't really fall (since there isn't anywhere to go). At that point you're just down to watching baking times and temperatures, which are easier to monitor.