https://www.mensfitness.com/training/cardio/why-do-my-lungs-burn-after-i-run-cold
https://www.runnersworld.com/ask-the-sports-doc/why-breathing-cold-air-hurts
https://wonderopolis.org/wonder/why-do-your-lungs-burn-when-you-run-in-the-cold
According to the above references it would appear that it's not so much the cold but the lack of humidity that causes the problem. And your baseline fitness can play a role... the harder and faster you breath the more likely it is to occur. So maybe on those really cold days you slow down a bit and don't breath so hard. Save the strenuous workouts for the warmer days.
