Should I insulate my basement ceiling?
What type of heating is used in that added on room? That will make a difference in how you solve the problem of the room being cooler than the rest of the house. Answer #1; yes insulate the floor if the basement under that room is unheated or cooler than the rest of the house. Answer #2; If the added room has 3 sides exposed to the weather, that is probably 1 or 2  more walls than any other single room in the house. If this is the case the room should have been built with more insulation than the rest of the house, since it will loose more heat due to the number of walls exposured. The type of heating system will determine how you correct the heating deficiency. You may have to add a separate heating device to solve the problem.