Artichokes can be frozen after cooking. Raw artichokes do not freeze well. Uncooked, artichokes will turn brown and mushy when thawed out. The cold temperature not only changes their color and texture but also their flavor (and they won't be pleasant). Freeze cooked artichokes in an airtight container or wrap them in plastic wrap and store them in a freezer safe resealable bag. Cooked whole artichokes will last for 1 to 2 months while cooked artichoke hearts can be frozen for several months.