I was Googling around, thinking about ways to fix my house up, when I found a question and answer column in which the contractor who writes the answers gived the following answer to a question:

The traditional and best location for the hot air heating register is under a window in an outside wall. The logic here is that the warm air in the room will collect at the ceiling. As it cools against the outside wall, a convection current will start down the outside wall and along the floor from that wall to the center of the house. Many people will assume that this 'draft' is the result of air leakage from the wall or window. By placing the heat source at the coldest spot, this convection current is counteracted.
(source (http://www.soundhome.com/consult/11to20.shtml))

To me, this explains a lot of the draftiness problem in our house. All of the heat registers are centrally located. None is more than 6 feet away from the cold air return (though they are in other rooms) except for the one in the attic.

Is this a job a DIYer could do? I know it would involve cutting holes in the floor and routing ductwork, which so far is a much greater scope of project than any we have attempted so far.

If not, would this be a fairly inexpensive job to contract for, or should I start scraping change out of my couch cushions?

Unfortunately, the proposed duct system would have to be verified and shown to be suited for the furnace. A Manual D calculation ACCA - Manual D - Residential Duct Systems - ISBN#1-892765-00-4 (http://www.constructionbook.com/acca-manual-d-residential-duct-systems-1-892765-00-4/acca-books/?CMP=KNC-Google)

A building permit would likely be required.

Thank you for your answer. I assume that by bringing up the fact that I may need a permit that you think this will be an expensive job. That's too bad. I have small children and I have to dress them in layers just to play around the house and even then they will have frozen fingers and toes. (I'm talking about in the deep of winter, of course, not currently.)

I guess I would need to start with a consultation from a certified HVAC contractor. How much do you suppose such a consultation would run me?

You might make your home feel a bit more comfortable by resetting the furnace fan to run 24/7 rather than just when there is a call for heat. The extra electricity to run the fan 24/7 is quite small. The fan running is actually cheap compared to the cost of starting a fan which draws up to 10x the power to start from a dead stop every time the heat kicks in. If you decide to go ahead with redoing your system some contractors will give you a free estimate, ask in advance.

This convection theory is one that I have not heard of, the reason I believe that the registers are placed below windows is two fold, first is to temper the cold drafts from the windows and because most people don't put furniture under windows to obstruct the register such as couches and chairs.
This type of duct system is called a perimeter duct system and is desirable in the heating season because the air induced at the outer walls is drawn through the room and back to the return grill versus close to the return and not getting to the outer portions of the room.
With a little instruction most people who are handy with tools could install their own duct.
Good luck , Mike