Does closing curtains 'make your home warmer'? I mean, in the sense that the act of closing curtains would somehow reduce the amount of heat loss of the house to the outside, thus making it warmer for a given supply of heating. 
 A: Assuming
1, you live somewhere that is colder outside than in
2, the curtain has finite thermal resistance (ie some insulating value)
3, the curtain is close enough to the window to reduce convection     
Then yes.
Try measuring the air temperature on the window side of the curtain, it should be lower than the room.
A: If the inside surface of the window is colder than the air in your room then the room will lose heat to the window. If this is the case then curtains will reduce the heat loss in exactly the same way that putting on clothes reduces the heat loss from your body.
Double glazing reduces the heat loss from windows, but even so a quick measurement in my living room suggests the inside surface of my (double glazed) window is colder than the rest of the room so curtains will make a difference.
But don't draw the curtains during the day because if the Sun is shining you'll get greenhouse heating of your room. If you draw the curtains the sunshine will heat the curtains, but they'll tend to keep hot air near the window where the heat can conduct outwards.
I did the experiment!
If anyone is still interested, I got up early this morning before the heating was on to measure the temperatures.
My living room has a window at each end, and I closed the curtains on one window and left the curtains open on the other window to act as a control. At 06:30 this morning the temperature in the room was 6ºC. When I placed the thermometer about a mm away from the uncurtained window the temperature was 5ºC, and 1 mm away from the curtained window (i.e. inside the curtains) the temperature was 2ºC. The temperature outside is about zero because there was a frost - I didn't go outside to measure it because it was too cold. Ask Francis Bacon about the dangers of such experiments :-)
So with the curtains closed the temperature at the window was 3 degrees lower showing that the curtains have a significant insulating effect. These are regular curtains, not especially heavy, so it's quite a big effect. I suspect it's not the thermal properties of the curtains that matters, but instead it's their ability to stop air currents from circulating cold air at the window into the rest of the room.
A: To some extent, the answer is yes; however, considering the characteristics of a curtain, the amount of heat conservation is negligible. 
