Can I add powdered, freeze dried strawberries to a sugar cookie recipe to make strawberry cookies?

I think it's worth a try! I've made this pea cookie recipe, which is a riff on Christina Tosi's corn cookies. Just use all AP flour instead of the pea flour, and powdered freeze dried strawberries instead of of the freeze dried peas. The flavor will likely be subtle, so making a powdered strawberry sugar (as Susan suggested) and rolling the dough balls in them could work to amp it up. Let us know what you come up with!

In case you decide to don your mad scientist hat, I think it would be fun to mix the ground strawberries with a sugar that you'd want to sprinkle onto the cookies instead of in the actual batter. Pink and sparkly.

I think it is possible to treat powdered strawberry as part of flour or addition, just like we use dried wheat flour (=AP flour) on baked goods. This recipe http://www.beantownbaker.com/2013/10/frosted-strawberry-sugar-cookies.html from google search does something similar. Maybe you can get inspiration from there?

Maybe leave your dried strawberries whole, find a sugar cookie recipe with raisins or other dried fruit, and use the strawberries instead. That way, you'll have ratios that work with dried fruit and the other usual suspects in sugar cookies.
And/or if you have some around, use the powdered as planned and garnish with fresh strawberries (if you have access to same).

I'm guessing it's up to you to play mad scientist here -closest I've ever come to powdered strawberries is strawberry quik. The world awaits your results; i woukd think it would take quite a bit of strawberry to make itself felt in a cookie; it might be easier to do a combo, such as strawberrry-orange.