The answer to this naturally will depend somewhat on your input method. However, there are some general principles.
The process of skidding occurs when one uses the skates to apply a great deal of force in the opposite direction from that of the skater's movement, and the skates break free. The key takeaway here is that this skidding process is a function of inertia.
The method you describe will tell you whether the input suddenly shifted 180 degrees, but that's not really what you want. What you want to do is determine if the input (which governs the forces the skater is applying) is in the same direction as the skater's momentum, or in the opposite direction. This will tell you if the skater is trying to speed up or slow down.
Depending on your input device, you may want to have a small region around this 180 degree point which causes a skid. It's impossible to reliably input exactly 180 degrees opposite something on most analog devices.