Here's the thing with All-Wheel-Drive and Four-Wheel-Drive vehicles. While they will help you to maintain traction during adverse conditions (snow, offroading, etc) they really do little to help with ice. The reason why is real simple - ICE IS SLICK!
AWD refers to how many wheels have the ability to transfer power from the engine to the pavement. On the Accord for example, it's Front-Wheel-Drive - meaning only the front wheels can drive the car. The two wheels in the rear simply free-spin and are not even connected to the engine. Rear-Wheel-Drive cars are similar, except in those cases it's the front wheels that don't contribute. All-Wheel-Drive cars can use any (or all) of the wheels to transfer power from the engine to the road.
AWD helps with traction during acceleration because it can evenly distribute the power among all four wheels... reducing the amount of wheel slippage. It can also transfer the power that would normally go to a wheel that has no traction to a wheel that does have traction. This is very good news if you need quick, stable acceleration - or if you need to navigate through extreme conditions (once again, such as deep snow or offroading conditions).
What AWD does *NOT* help with is sliding. Most accidents on icy roads are due to cornering or slowing down - NOT accelerating. When there is no power being transferred to the wheels, then AWD makes no difference whatsoever. Instead one must rely on other technologies such as stability control, Anti-lock brakes, and advanced tire technologies (such as used in specific snow/ice tires). Sometimes advances in these technologies go hand-in-hand with cars that have AWD (Such as the Audi) but this has little to do with the actual AWD itself. Another thing people almost never mention is driving experience and driver's education. Personally I believe that a driver who knows how to handle a vehicle under adverse conditions will be MUCH more effective than any of these advanced technologies.
It is a common misconception that AWD/4WD vehicles are safer and handle better on snowy/icy roads. This is simply NOT TRUE! If anything else it often installs a false sense of security in the driver which can lead them to push the envelope too much and actually increase the risk of an accident. If your parents are considering an AWD vehicle based SOLELY on the presence of snow/ice on an interstate for a few months out of the year then they are most likely going to be sorely disappointed.
And as previously mentioned, AWD vehicles get less fuel economy than their Two-Wheel-Drive counterparts. Especially with the price of gas these days this can lead to them being significantly more expensive to operate. If money is an issue then perhaps your parents should consider purchasing a good set of snow/ice tires to use in the Winter months instead of purchasing a whole new car.