Jump racing is all about keeping warm and dry during the winter months. Many racecourses suggest that you dress for the weather, although in Premier Enclosures and Hospitality the dress code is still often smart casual so it is always worth checking.
During the summer Flat racing season you will be more likely to see the ladies in hats and fascinators and dresses. A strict dress code is only enforced at a handful of fixtures such as Royal Ascot, The Derby and Glorious Goodwood. In the summer you are advised to dress in Premier Enclosure for a smart occasion, such as a wedding. However, in the Grandstand Enclosure it tends to be far more relaxed and you can dress casually. It is worth always checking the individual racecourse websites, though.