A/C in cold weather

I just bought my avalanche a week ago. Its an 08 LT Z71 and I went to test the AC but when I click the button it blinks a few times and then doesn't turn on. I live in new england and it hasnt been warmer then 15 degrees so I think it may be a product of the sensor saying that it is actually too cold for AC. Is this correct? Or should my AC work? I am not use to all the technology in a truck. I had an 04 basic chevy s10 before so all of these sensors and such are throwing me off. I feel like when its this cold turning the AC on it will automatically turn it off because its so cold. Is this correct?

I have a 2013 and the AC turns on automatically when it's 40 degrees or higher and the light is off when less than 40 degrees and I don't believe you can turn it on manually so your 08 may work somewhat the same.  It should be in the manual if you have one.