Rather than being the son of a Nazi supervillain who embarked on his own nefarious path, the MCU’s Zemo is a former Sokovian general whose family was killed during the Avengers’ battle with Ultron in Sokovia, which saw the country’s capital city, Novi Grad, being destroyed.
Still, considering how much Zemo’s backstory was altered for Captain America: Civil War, it’s not surprising he didn’t wear any kind of costume.
Blaming Earth’s Mightiest Heroes for the death of his wife, son and father, Zemo initiated a plan to turn the protagonists against one another, which included framing Bucky Barnes for his attack on the United Nations.