Does the Catholic Church allow Catholic weddings (i.e. weddings canonically recognized by the Catholic Church) to take place outdoors, even if one of the couple is not Catholic? If so, is there any specific permission that must be granted to ensure the wedding is recognized, and must this permission be granted by Church officials where the couple lives, or where the wedding will take place?
Can. 1118 §1. A marriage between Catholics or between a Catholic party and a non-Catholic baptized party is to be celebrated in a parish church. It can be celebrated in another church or oratory with the permission of the local ordinary or pastor.
§2. The local ordinary can permit a marriage to be celebrated in another suitable place.
Thus, according to §2, you would need permission from the "local ordinary" (bishop) to have a wedding somewhere other than in a Catholic church.