Works fine with headwear. I live in Canada - when it's cold the warm fuzzy hats (aka "toques") come out. Never had an issue.
One thing to note about Face ID - if it doesn't recognize you correctly, it will prompt for your password/PIN. When you enter it, Face ID updates its database with the image it just took, so that it can adjust to changes in your appearance. eg: It might not recognize me with a full beard today, but tomorrow, it will.