Yes, the idea with secondary air injection is to inject more oxygen to get the exhaust to combust more completely and heat up the catalytic convertors while the engine is cold. It is not needed once the engine is warm.
It is true the air pumps can freeze from moisture getting in them in cold climates. Not very many cars in WI have air pumps, since they are usually only used in low emissions cars like you would have in CA. I will admit I haven't really come across air injection very often here, so I may not be as knowledgeable about the functional stuff.
However, you have a circuit code, which is an electrical problem (what I specialize in), so a frozen air pump would not cause the code (unless the freezing somehow damaged electrical windings in the pump). Again, basically the PCM
is seeing voltage being sent to the air pump when it shouldn't be seeing it. So it will require some electrical troubleshooting to fix.
Here is the wiring diagram: http://www.revbase.com/BBBMotor/Wd/D...9-67ff21739dce
The air pump relay is located in the relay center box 1, which is right next to the battery. It would be the smaller relay at the bottom. It might be stuck open, so you could try swapping the relay or replacing it to see if the code goes away or changes.
If you know what you're doing, you can jump the relay and get the pump to come on with the car off to see if it's working.