Taking their coat means defeating someone in debate or banning them from an Internet forum. Putting on a coat is synonymous with taking the red pill. The terminology began when Trump suggested that a protester be thrown from his rally, without their coat, into the cold.
You may find Trump supporters making comments like "take a coat" or "give this man a coat!" and it has nothing to do with fashion or cold weather. In January 2016, at a Trump rally in Burlington, Vermont, Trump was briefly interrupted during a speech by protestors. His response was to basically shrug them off and tell his security to, "throw them out. Throw them out in the cold... don't give them their coat." Trump, insistent on keeping their outerwear, continued: "No coats. Confiscate their coats." Nimble Navigators all over the web have embraced this moment and refer to 'taking a coat' as a sort of reward. For example, if one were to say "I've switched my support from Bernie Sanders to Donald Trump," the response would be, "give this man a coat."
Not wanting to miss a pun opportunity, Reddit's Donald Trump community has raised over $15,000 for Operation Warm, an organization that provides coats for families in need.