None of the masks we reviewed are cotton, and for good reason. Cotton retains moisture, which means it can freeze your breath. It can also collect snow and work against you when your body is trying to stay warm.
Whether you desire a synthetic blend of polyester and spandex fabrics or merino wool is a personal choice, keeping in mind that merino wool is great for breathability and its antimicrobial nature allows it to dry quickly and not get stinky, while synthetic materials can be combined and woven in ways that can better block against wind and external moisture like snow.
When in doubt, doubling up and either carrying an alternative in your backpack or wearing them as layers, such as a Smartwool Thermal Merino Reversible Neck Gaiter over a Blackstrap Hood Balaclava, is never a poor option, budget-dependent.