There's something more going on here than just the altitude

I only once had to adjust a cookie recipe, and that was for a chocolate chip that had too much butter.

Make sure to use either butter or a really good margarine, not the diet spreads, and if a recipe calls for either butter or marg, don't substitute Crisco.

Check the temp of the oven.

Roll the dough for cut-out cookies on a cold surface (I chill my pastry board), and keep them cold until they go in the over. Keep the amount of rolling to a minimum.

Hope all these help