Can I delete Ultimate Chicken Horse without losing all my progress?

Solution 1:

Yes you can.

You safely delete any and all of your games and reinstall them tomorrow, next month, or 3 decades from now (as long as servers are still up) and keep all of your saved data from that game.

This works because your games are all backed up to your account on Microsoft's Xbox servers.

You can also delete your saved data!

To do this you'll want to go to My games & apps, go over to the app you want to remove, press the Menu button on your controller, scroll to Manage game & add-ons, then to the Saved Data box, and then delete it.