One of the first things my instructor told me was "I hope you're getting your license for fun or a job, and not planning on commuting. Eventually you'll get stuck somewhere due to the weather."

Heavy, powerful commercial jets have deicing systems. They also have the benefit of an entire team of air traffic controllers on takeoff and landing -- and they still get grounded by weather. Small planes are grounded by such inclement weather as "fog", "thunderstorms", "high winds", and "low cloud cover".