Modern high-tech diesels can not completely compensate for cold temps with perfect driveabilty. My engine makes some light 'nailing' noises on cold starts (25F or less). The noise and lack of driveability is a combination of improper combustion from a cold combustion chamber mixed with injectors that are way past new, but not worn out. Some things that reduce the noise and improve cold start drivability:
After starting the car wait at a bit (~30 seconds) before taking off. If you have more time to wait, then wait. A few minutes really helps a lot. You are already doing this. In a cold start case, patience is a virtue.
Add an all-in-one winter fuel additive (cetane boost, anti-gel, lubricity additive, and solvent). Cetane boost helps a lot for those cold starts. Winter fuel is blended for cold flow (more kerosene content), not for increased cetane which really helps cold weather starts. Use whatever brand is on sale. I pour in a lot, as much as 3x or 4x of the recommended dose. Typical 1 quart/liter bottle usually treats 100 gallons, so yes, I'm almost pouring in the whole bottle. I'm overdosing the fuel but all I'm doing is wasting some money for the cause of maximizing the effect (easier starts), it does no harm to the engine. This is a lot cheaper than replacing fuel injectors. It reduces the cold start noise a lot.
The CR TDIs have a very sophisticated injection cycle, up to 7 injection events per power stroke. The design works well regardless of temperature. I have never had my glow plug light stay on for more than 5 seconds and the engine starts immediately and idles smoothly. I don't hear the nailing until I drive off. The CR is a fabulous piece of technology that has stupid easy cold start capability compared to my last TDI, a 96 Passat with a 1Z engine. On that beast I would have to wait around 30 seconds or more for the glow plug light to go off, crank & crank the starter as the engine rebelled against starting, then it would chug, cough, shake, sputter, and fight combustion while copious amounts of acrid white smoke came out the exhaust. The old Passat always started, but it sure was a damn ugly process.
Your car is fine and running as designed. Physics dictates cold temps and starting a diesel do not get along, even with all this wonderful technology. Drive more and worry less.