The HOW STUFF WORKS site has information that will help in understanding the problem. The description includes:
"The cold side, consisting of the expansion valve and the cold coil, is generally placed into a furnace or some other air handler. The air handler blows air through the coil and routes the air throughout the building using a series of ducts. The hot side, known as the condensing unit, lives outside the building. In most home installations, . . . "
When you combine that with the Wikipedia picture, you can see what should be cold and what should be hot.
The original post describes the unit as a "Central A/C unit"; not a reversible heat pump.
The compressor is outside. It takes cold gas from the evaporator (inside) and compresses it, after which it is condensed to liquid. The large pipe is supposed to carry the vapor from the evaporator (low density, therefore larger pipe) and it is cold but should not be below freezing. It has just come through the evaporator coil with air blowing over the coil, which should make it well above freezing.
The small pipe returns the liquid refrigerant to the evaporator where it goes through the expansion valve. The liquid should be at high pressure and should never be below freezing under any imaginable circumstances if the equipment is working.
Since the expansion valve is usually inside with the evaporator, it may be that the expansion valve has failed open or is open by command of the control system. Another possiblity is that there is something in the condenser that is plugging the liquid refrigerant return. It is also possible that much of the refrigerant has leaked out of the system but there is still enough left to get some cooling. If the evaporator is calling for more refrigerant from the expansion valve it could expose the liquid return pipe to low pressure on the suction side of the compressor.
Those are the only things that would produce frost on the small pipe.
Freezing temperatures and frost on the pipes can only occur when the compressor pressure is so low that the evaporation temperature of the refrigerant is below the freezing point.
The one thing that is certain is that the unit must be serviced.