To mull something over means to think about it carefully and thoroughly. Mulled can also describe a drink that's been heated with spices. Mulled cider or mulled wine means the liquid has been warmed gently with cinnamon, cloves, and other spices that make it taste rich and comforting on a cold day. The spices need time to blend into the drink, just like ideas need time to come together in your mind when you're mulling something over.