For the Signature Dining Restaurants, a "Business Casual" dress code is in effect:
Men - Dress pants, jeans or dress shorts and a T-shirt or long sleeve shirt with collar is required. (Jackets optional.)
Women - Jeans, skirts or dress shorts and blouse, sweater or dress is required.
NOT PERMITTED: Tank tops, swim suits or swim cover ups, hats for gentlemen, cut offs or clothing with rips/tears are not allowed. T-shirts with offensive language/graphics will also not be permitted.
Probably depends on the weather, long trousers might be required in January but they definitely aren't required in August
The only restaurant at Disney where shorts and a collared shirt are not sufficient for a gentleman is Victoria and Alberts, and come to think of it V&A only requires gentlemen to wear a jacket, they don't specifically mention shorts but I can't imagine anyone attempting to enter V&A's wearing shorts