Yes, it's possible to freeze oregano. Wash and dry the fresh oregano sprigs after removing them from the stem. Place them in a plastic bag, remove the air, and put the sealed bag in the freezer. Another option is to mix chopped oregano leaves with a small amount of water and put them in ice cube trays. Put the trays in the freezer for a few hours, remove the frozen cubes, and place them in a plastic bag. Either way, the frozen oregano lasts for up to one year.