First, you need to know the minimum amount of power in Watt*Hours (or kWatt*Hours) that the emergency loads require...
For example, lets guess that the your central heat requires 600 watts and runs 4 hours per day to keep your house minimally warm (your need to measure this somehow--if you don't know how, you should get a friend or electrician who can). Also, you may wish backup power for a fridge/freezer and a few lights/radio.
For general appliances (in the US), you can always use Kill-A-Watt meter ($25-$40 each)...
In my example, the result would be 600 watts * 4 hours or 2,400 Watt*Hours (2.4 kWH if you are reading your electric meter/bill).
Next, you need to figure out how much sun you get in your area. One place to look is here:
http://rredc.nrel.gov/solar/pubs/redbook/
As you look through the data (I would suggest using the PDF files--they are easier to read and understand)--you will find that, usually, there is a difference in that number of hours of sun per day based on month/season... So, lets assume you need heat in the winter and your area gets 3 hours per day of sun...
Based on average efficiencies of charger, batteries, and inverter, you get about 60% overall system efficiency:
Solar Panels=2,400WH/D * / (0.60 * 3Hsun/D)= 1,333 watts (PTC) of solar panels.
Add about 13% for PTC (real solar energy) to STC ("data sheet" solar ratings):
1,333*1.13%=1,506 watts (STC) of solar panels... That is about $7,500 of solar panels (at $5/watt--you can probably find them for $4/watt or a bit less)... (excluding all of the other costs for Charge Controller, batteries, replacement batteries every 5-10 years, inverter, installation)...
If your furnace runs on natural gas, you might be better off just installing a small home backup generator that runs off of natural gas for less money and higher availability (if you have natural gas, you have heat and fuel to run your generator--if you don't have natural gas, you don't need to run the generator--and with solar, your might lose your power when you have little sun, so solar panels become less useful).
A better "investment" for you money might be to go with a Grid Tied system (or Grid Tied with battery backup). You would really like to use your solar system's panels 365 days per year to generate power for daily use--rather than use it may be one or two weeks per year when you have ice storms (or whatever knocks out your power).
What you are asking for can be done--but it would probably be better if you approached it from another angle (full solar power system for home, and/or backup generator). Money wise, just creating a solar system for
emergency backup power (used only a few days or weeks out of the year) does not give a good return on investment.
Or just install several vented gas wall heaters (that don't need AC power) in a couple of rooms to keep the home livable during cold weather.
-Bill