Are curtains effective for keeping the room warm?
Curtains or drapes can help insulate a room. One of the main methods is to reduce the amount of air exchange between a cold window and the rest of the room. 

Air in a room is always trying to equalize itself. The cold air at a window mixes with the warm air in the rest of the room.  If you trap the cold air behind a poor conductor (such as an airtight drape) the rest of the room air remains warmer.

Most cloth is a poor conductor (not good at transferring heat). This is a good thing.  The effectiveness is largely based on how airtight the cloth is and how tightly it fits to the window on all sides - the top and floor as well as the lateral sides.

Many curtains are advertised as thermal.  In general, they are fairly thick and have an air barrier to block flow through them. Fitting is as important as the material. In addition to going floor to ceiling, try to tightly fit the curtain to the walls on either side.