Its always possible to add another layer of clothes, unfortunately the opposite cant be said.
A jacket will not prevent the cold air from hurting a respiratory system. After 1 hour with such cold AC, I will get a sore throat, and come back home with a heavy headache.
It's pretty hard to code in a winter jacket, I've tried when being in an office set to 18°C. I absolutely can't work below 22°C and will refuse to work at those temperatures. (But then again, I'm a woman)
Luckily the french have a law saying that you shouldn't heat above 21°C and shouldn't cool below 26°C, and I'm a huge fan of this law, everyone should adopt it.