What you’re describing is the hood on a casual sweatshirt.
Hoods have to fit tightly against your face so this doesn’t happen. It also helps if the coat zips up to your chin, otherwise the hood is a giant gaping hole in front of your neck. Another feature is a fur lining. The insulation the fur adds is negligible, but it creates a very large boundary area, resulting in a lot less convective heat loss (only if the hood fits properly, otherwise it’s kind of pointless).
The issue you run into is that a lot of manufacturers want their products to have a larger market, so they try to balance function with form. Fur lined hoods aren’t stylish; they look out of place if your just driving your Prius to Bed Bath and Beyond. So you can suffer for a few minutes in the parking lot with a North Face puffy and it’s no big deal.
Pic is a random image of the Patagonia Houdini, and extremely popular wind jacket. Notice the hood conforms to the wearers face. There’s very little gap under the chin or near the cheeks. There’s no fur lining because it’s designed as a lightweight option rather than the Arctic -30° temps other Anons have posted.