It all depends how you're drifting, and what the conditions of your drifting are.
There are three basic ways to drift a car, and all can be used in combination with each other - depending on how skilled a driver is, or what they're trying to do with the car.
1) The first and simplest is by using the steering wheel alone. Come into a corner, adjust the car slightly to one side, and then quickly re-adjust it to the other direction by flicking the steering wheel. This will kick your back end out (ideally), into a semi-slide. This method produces (in my experience) the least effective drifts on it's own, but if you combine it with the others, it adds to the effect quite nicely.
2) The handbrake drift. By using the e-brake, the driver has the ability to lock and unlock the back wheels of the car as they please. By locking the back tires, they are effectively putting the car into a skid similar to what kids often do on their bikes, by locking the back tires and kicking out the back end. This can give very sudden and aggressive slides, but if you aren't familiar with feathering the handbrake, it will end quicker, as the brake tends to bring the car to a stop.
3) Using the accelerator. This is my favorite method of drifting, as it provides the driver with the most control, as well as the longest drifts. Come into a corner at a desired speed. As the car begins to round, use the accelerator to break the wheels free of traction by over-gassing. Be careful with this method, as it tends to require semi-consistant conditions (if you hit a hard patch, your wheels can catch and throw your car in a direction that you may not have anticipated). Practice this in a parking lot first, as it requires getting used to. However, once accustomed to it, you can use the gas to kick your back end further out, or to bring it back in (with more or less power, respectively) - all while focusing on steering to keep your car perpendicular to your direction of choice. Using the aforementioned 'flick' technique in combination with this technique is particularly effective, and is referred to as the Scandinavian Flick.
All of these techniques become easier with the less traction on the ground (however, too little traction just leads to full spins). As I said before, practice in a parking lot first.
I just realized that I haven't really answered your question...
Using the e-brake to drift will in time wear away at your e-brake, but it isn't really bad for the car as the e-brake is easily fixable (unless you're using too much gas in combo with the brake). Using the gas to drift can be particularly harsh on your differential, especially in cars with 4wd and AWD (ESPECIALLY AWD). IT also becomes worse and worse for the car with more and more traction on the ground. (the more snow/ice, the less bad it is).
Hope that helps.