I have done both. I have dried off and bundled up before running. I have also just hopped off the bike and ran. Mostly, I just don’t do a lot of bricks when it’s super cold.
One way to think about it is you are going to sweat while running in the cold, correct? So does it make you more susceptible to getting sick by starting sweaty, or getting sweaty during the run? Either way, you are sweaty and cold 