What used to be called a conservatory here in Victorian times is a sunroom, greenhouse, garden room. In the last mid-century, people added on or built Florida rooms in the north, which are usually glassed in, unheated three-season porches. Some of those have been modified and heated and are sunroom/garden rooms now. A mudroom here is really a room to come inside when you are a mess, muddy from the garden (or mud season, which is what spring in New England is called), or messy from the snow. You use it to clean up before going into the house, and store and dry outer winter things.