With asphalt driveways, you don't need to worry about damage caused by using salt to melt the snow. Salt will melt the snow as it hits and continue to work well below freezing temperatures. This used to be the only method of treating a driveway to prevent ice and snow from accumulating. Now, there are several other methods to try if rock salt doesn't work. Look for salt that specifically lists "sodium chloride" in the ingredients. The drawback to rock salt is that it can destroy vegetation and ruin concrete.
Calcium and potassium chloride melt faster than rock salt. While both chemicals will corrode concrete driveways, they are safe, inexpensive and easy to use on asphalt driveways. However, they do not always work in extreme temperatures. Magnesium chloride may be used on concrete driveways and causes less damage to vegetation. Since you are trying to reduce icing on an asphalt driveway, magnesium chloride provides the most benefits.
Before the snow falls, if you cover your asphalt driveway in sand, you can reduce the formation of ice and prevent slippery situations. Unfortunately, it will be a mess to clean up when the snow thaws and takes a considerable amount of time to employ. It can also become extremely messy. While the sand won't turn to mud, it will cling to your tires and scatter easily to other areas of your lawn. However, it does do the job of preventing ice from forming on your driveway and won't harm the asphalt.
Heated driveways can be installed to prevent the need for shoveling and salting. Radial-heat systems prevent snow from sticking to the asphalt driveway, saving you a significant amount of time. If time is more important than money, these systems require no maintenance and can be turned on and off as needed. The drawback is that you will need to install these systems before you pave your driveway. However, the added safety may be worthwhile when you consider that falling on ice can be very dangerous.