It sounds like what you want is a set of heat loss calculations. These are the calculations a heating contractor would do in order to determine how much power (BTU output) a furnace/boiler would need in order to keep your house warm. A heating system is then sized such that it can overcome the heat loss your home would experience on the coldest day of the year.
These calculations are based on the area of each room, exterior walls, number of windows and doors, type of insulation, etc. I saw an episode of Ask This Old House that included a heat-loss analysis using software that calculated this using a house model / floor plan entered by the contractor. According to this show page (http://www.thisoldhouse.com/toh/tv/ask-toh/products-and-services/episode/0,,20321333_20311273,00.html), that software was made by WrightSoft.
Unfortunately, this software seems to be aimed at contractors rather than homeowners, and has a price tag of $200-$500. It is also probably rather technical. There are some other options, including some free online heat loss calculators. But why bother, when you can probably have a heating or insulation contractor come to your house and do these calculations for you?
In Massachusetts, where I live, the utility companies offer an energy audit service where, among other things, they inspect and measure your house and offer you various options for adding insulation. For each option, e.g. blowing cellulose insulation into the exterior walls, they also list the estimated savings per year, based on local energy prices. Using that, you can calculate how many years it'll be before the insulation work pays for itself. In my case, about $2000 of insulation work would pay off in between 2 and 3 years.
If utility companies in your state don't offer this service, you may still be able to find an insulation contractor who can. And for figuring out which doors to close to reduce heat to unused rooms, why not do some experiments? You can buy a thermometer with multiple remote sensors, and watch how the temperature fluctuates in your unused rooms.
Yes, the room can be very cold because of the floor.
Concrete slabs do not insulate well (R-value around 0.6!), and they lose most of their heat along the outside edge of the slab (the ground beneath the slab is a decent insulator). Using a Heat Loss Calculator, I assumed you had a 10x10 room with a completely uninsulated floor (concrete), uninsulated walls (stick built w/drywall), and ceiling (drywall ceiling with an uninsulated attic).
Heat loss was 4050 BTU/hour from the floor, 5440 BTU/hr from the walls, and only 1540 BTU/hr from the ceiling.
So, while your ceiling may be a factor, it's probably not the most major factor. Given that your floor is very cold, you probably don't have much (or any) insulation on that slab.
On the outside of the building, see if you can see the edges of the concrete slab. If you can, then it's not insulated. Buying some one-inch R-5 foam insulation and affixing that to the perimeter of the concrete slab drops the heat loss from 4050 BTU/hour in half to 2050 BTU/hour. Two-inch, R-11 insulation drops the heat loss to only 1050 BTU/hour.
Placing a rug on the floor would likely be insufficient, as carpet only gives an R-value of around 1.3 (and an area rug isn't going to cover the entire floor, anyway).
Edit with more information:
Consider a house built on an uninsulated concrete slab. Insulating the slab can lead to a reduction of 10-20% in total heating costs. Of the heat lost through a concrete slab, up to 80% is lost through the exposed outside edges.
Best Answer
There are heated floor mats that you can buy. We use them at desks in our warehouse. There's not much of a color choice but sizes do vary. You can either get them at office supplies or diy's. Search for 'heated floor mats' for internet goodness.