Leave room around the collar
A high coat collar and a large, low-sitting hat can cover a substantial area around the face. If that feels too enclosed, first change the hat position or collar where this still preserves the protection you need from the weather. An additional thick scarf can alter the arrangement again and should be included in the try-on.
Open lapels leave more of the top visible. The hat can pick up a colour from that top or provide an accent of its own. Check the coat open as well if you often wear it that way. The outfit need not look identical in every position, but its usual versions should feel right to you.
Compare volume and surface texture
A chunky knitted hat has a different visible texture from a smooth one. Alongside a strongly textured coat, both surfaces may be prominent. If you want less visual activity, try a quieter surface before changing the colour. Texture may have been the more noticeable difference.
Look at the shape from the side too. Extra fabric at the back, a broad turned-up edge or a pompom changes the outline. None of these shapes belongs exclusively to a particular face shape. The effect you want and a fit that does not need constant correction during movement are more useful considerations.
Think through the whole journey
Put the hat on and take it off again. If there is nowhere to leave it at your destination, consider where you will store it without forcing it into a tiny bag. Include glasses and headphones in the comparison if you use them outdoors.
Between two hats you already own, choose the one that works with both the coat and the day's activities. You do not need a new shade simply because a styling photograph matches it exactly to a handbag. The combination you actually wear matters more than a colour match viewed in isolation.
