It depends a lot on your climate and probably even more on how well your home is insulated and sealed.

You can start to get a rough idea by running this home heat loss calculator:
http://www.builditsolar.com/References/Calculators/HeatLoss/HeatLoss.htm

Have a look at what your outside temps are for a typical winter day (don't use the worst case).  Weather.com has this kind of data.  Put this average overnight temp in as the "Design Outdoor Temperature" input.  Fill in all the insulation levels etc.
When you do the calculate, the "Design Loss" output column will give you an idea what the heat loss per hour is at that temperature.
To get the heat loss for the full night, just multiply it by the time overnight -- maybe 12 hours.  This is the amount of solar heat you would have to store to heat the house overnight.  I used 12 hours instead of something like 16 hours because you can get the house a bit on the warm side during a sunny day with the air collectors (hopefully), and coast a while on this as there is some stored heat in the house thermal mass, and you probably will setback the night temp a bit.

To get an idea (very roughly) how much water collector this might require, figure that on a sunny day, 1 sqft of collector might see about 1700 BTU of solar radiation -- if you do a descent collector, about half of that will get into the storage tank -- so, about 800 BTU stored per 1 sqft of collector on a sunny day.

So, if your overnight loss was (say) 80,000 BTU, then you would need about (80000/800) = 100 sqft of collector to store enough heat on a sunny day to heat the house overnight.  

A storage rule of thumb is to use about 1.5 to 2 gallons of water storage for each 1 sqft of collector -- about a 200 gallon tank in this case.  This amount of storage will store the heat you collect over one sunny day.  

If you want to accommodate cloudy days, then you need both more collector and more storage.  Its tough to accommodate a lot of cloudy weather, and most solar heating systems don't try, and just use a backup heater for cloudy periods.

As you will see when you run through the heat loss calcs, good insulation and sealing make it much more feasible to get a good solar heating fraction.