What classy piece of clothing can you put on top of a shirt for warmth?

There are suit jackets but they are not the best for warmth and they can look a bit "too much" sometimes. I'm looking for something that fits a "classy" look. I heard trench coats can look good with classy outfits.
What classy piece of clothing can you put on top of a shirt for warmth?
What classy piece of clothing can you put on top of a shirt for warmth?
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