Is a little ice on the cooling coils ok?
The suction line (the larger pipe) should never be iced up during normal operation.  By the time the refrigerant gets to the end of the evaporator coil, it should be completely boiled off (in a gas state).  The bottom few coils may frost up,  but the top ones should only be sweating at most.
If the suction line; or more than the bottom third of the coil, is frosted up.  You either have an overcharged system, or you're not getting enough air flow over the coils.
Make sure all registers and returns are open, and unobstructed. Check all filters, to make sure they're clean. If you have a multi-speed blower,  make sure it's set to run at the proper speed. And make sure it's actually running at, or near the speed it's supposed to be running at.
If none of that helps, have an HVAC technician check the refrigerant level.
Normal System

Temperature and pressure are the same thing in a refrigeration system, so based on the pressures shown above you can easily determine the temperature of the refrigerant .  Assuming this is an R22 system, you'll see that the refrigerant enters the evaporator at 26°F, and leaves above freezing at 43°F. The suction line in this system is above freezing, so no icing will take place. The temperature may be below the dew point, so there may be sweating (condensation).
Not enough air flow

In this example you can see that the refrigerant enters the evaporator at 26°F, but it leaves the evaporator below freezing at 31°F.  Since the suction line in this case is below freezing, there may be frosting/icing of the line.  If the temperature of the line stays below freezing all the way back to the compressor, you'll see icing all the way along the line.
In this case, there's not enough air flowing through the evaporator. Because of this, not enough heat is being transferred to the refrigerant.
Overcharged
Sorry, I don't have an image for this. In this situation, you'll see that the temperature of the refrigerant entering the evaporator is so low. That even with good air flow, enough heat cannot be transferred to bring the refrigerant above freezing.
undercharged
While icing due to low refrigerant is rare, and often requires other problems, it can happen.  Because the pressure in the evaporator is so low, the boiling point of the refrigerant is well below 32°F. This causes the coils closest to the metering device to be very cold, which causes moisture to freeze. As the coil freezes, air flow is restricted. As air flow is restricted, less heat is removed from the refrigerant. The freezing slowly creeps through the coil, and eventually makes its way back along the suction line to the compressor.