Just got my 2014 CTS 2.0T AWD Lux with 17" wheels/tires in September. Have 4,300 miles on it and live in Buffalo NY and we've had quite a bit of snow here this winter. I'm on my first season so its done very well in the snow, but there are certain types of snow and slush that can lead to some slippage for me as well particularly the slushy mushy variety (thats a technical term by the way

). When I notice slippage that seems to be pushing the car around while it attempts to gain grip I'll slip it into Ice/Snow mode which has helped a lot. Overall though its pretty stable. I have played with it a bit in a slippery stop condition and its RWD bias nature will let the tail start to go one way if you slam the gas from a stop on ice or packed snow. I came from a 2012 A4 Quattro and had a similar sensation though the Cadillac is even better in the snow than the Audi was with stock all season tires. On both cars I also noticed they first apportion power between the front and rear axles via the center differential which is almost seamless in many cases and you may barely feel it as it makes virtually no noise from within the car or sensation. If you're seeing the traction/stabilitrack light come on often then you're likely either getting enough movement or yaw to one side that its correcting or more likely its also applying traction control to slow down a spinning wheel or wheels in addition to using the center diff to apportion power which means you are lacking some substantial grip.
That all said, one season can make a difference even though your tires still have very low mileage on them. Temperature makes a big difference too. If you're experiencing very low temps in low teens or single digits that may make the rubber even harder which affects the grip since all seasons don't stay as soft in the snow to grip like a snow tire does.
Lastly, both my Audi and the CTS with their rear bias nature will let the tail wag if you give any power while in a turn so you do have to take it easy. AWD vehicles only give a slight advantage (some may argue none) to 2WD vehicles when it comes to turning. For that it all comes down to tires.
All in all, your AWD may be just fine, but if you apply too much power in a situation where all four tires are in a low traction situation you may still end up sliding a bit as the car works to apportion power and try to find grip.