Aircraft operating in icy conditions are equipped with de-icing equipment to remove ice from specific parts of the aircraft (wing, sensors,...) in flight.
When there is snow or icy conditions while the aircraft is still on ground, it is de-iced with ground equipment (de-ice fluid, towel,...).
Is the aircraft's own de-icing equipment also used?
Is this equipment enough to de-ice an aircraft before take-off (lets say if this is a sunny day and the temperature is just below 0°C)?
Usually, no.
There are two main methods used to deice an airplane in the air. One is letting warm air that is bleed from the jet engine to heat the wing leading edge. The other is to have have rubber air bladders (called deice boots) on the leading edge of the wing and tail surfaces that are pumped up and the ice falls off. Both of those methods are only useful to deice the leading edge of the wing and tail surfaces which is pretty much the only dangerous place where an airplane can gather ice while it is flying.
Airplanes on the ground are a different story. Ice can be built up pretty much anywhere as there is no airflow to prevent it. Excessive ice on control surfaces can make them behave "unevenly" or in extreme cases even unresponsive. Bigger chunks of ice breaking off the fuselage can get ingested by the engine and cause problems. It is therefore important that the airplane takes off ice-free. In fact, as little as frost on the surface of the wings can cause a significant loss of lift and can even cause a plane to crash.
Yes, anti-ice equipment is sometimes used on the ground, but is usually not sufficient to clear the plane of ice.
Airplane systems are generally referred to as anti-ice, because they are designed to prevent ice from forming or accumulating. Airport equipment is referred to as de-ice, because it is designed to remove ice as well as preventing it from forming (to some degree). So, as others have said, the real de-icing equipment available on the ground is much more effective than what is on the plane.
Anti-ice systems are generally designed to protect key areas of the airplane where ice is most likely to form in flight; leading edges of the wings, engine cowls/props, and pitot-static or other sensors. However, on the ground, it will accumulate on other exposed surfaces like wings/stabilizers/fuselage. This is why the de-ice measures are needed, to clear off those surfaces as well, because ice on the wings is bad.
However, anti-ice equipment may be used on the ground as well when needed. Air Florida Flight 90 crashed shortly after takeoff in icing conditions, and a contributing factor was ice accumulating on engine sensors which prevented the engines from providing full thrust. So when icing is expected, the anti-ice systems will certainly be used on the ground to provide added protecting to the most critical surfaces, in addition to the protection from de-icing procedures. Failing to have the wing and control surfaces properly de-iced also contributed to that accident.
Also, see this related question: Why turn off pitot tube heating?
