Hii, I was away from QL for some time.. now 'm back. read your post.. tell me a few things before heading to the issue.

Model Year
Kms done
Recent service hystory
Since how long r u with the car

Now to the issues.
1. A/c cooling effect.
The force of air flow? I hope you might have been checked all related with a/c. If gas and all ok for sure, better do clean the duct. Its just inside the glove box. May be thats dirty.

2. Starting problem.
Before making any sudden decision, replace your battery with any of your friends and make a try. Probably the battery may show green, but the amps will not be correct. Its normal issue with the battery at this weather.

or. check the dynamo/ dynamo connection cable. may be its loose or near to break.

or. if the symptom like struggle start when the engine is hot, check the fuel injectors. clean it. before doing this, check the plugs.

Hope you have a clear idea about your rexton..! Follow above points... i hope no other issue may be there on this car.