That is normal. It takes a few minutes to adjust.

 

The temp sensor needs time to get good info. If you leave the car in your garage it will take some driving time to get an accurate ambient temp reading.

 

The temp not being accurate is normal, although annoying.

 

I was always under the impression that running the AC when it's cold outside will ruin the compressor. Apparently, with the G, this is not the case. The AC light coming on is a normal part of the auto climate control function. As mentioned several times earlier, just press "Auto", set the temp and forget it. If the temp gets comfortable and the fan is still blowing a little too vigorously, just dial down the temp a few degrees. The climate control system does a great job once you learn to just leave it the hell alone

 

Running the A/C when it is cold out will not damage the compressor. In fact not running the compressor for a longer period (like for several months over the winter) will damage the compressor,letting corrosion set in and drying out seals. Most newer vehicles including the G will cycle the A/C automatically almost no matter what temperature when in defrost mode. This is a safety precaution for the A/C compressor so it gets some use and is also more effective in clearing moisture from the interior windows.