Does Modern Warfare II have crossplay? Call of Duty: Modern Warfare II does support crossplay on PlayStation 4, PS5, Xbox One, Xbox Series X, and PC (via Steam and Battle).
The good news is that Call of Duty Black Ops: Cold War does support cross-platform options such as cross-play and cross-progression. Simply put, you will be able to play Cold War with your friends regardless of which platform they're on.