Final answer:
Henry Winkler's character on 'Happy Days' was named Arthur Fonzarelli, also known as 'The Fonz.' He became a cultural icon of the 1970s and 1980s through the show.
Step-by-step explanation:
The full name of Henry Winkler's cool character on "Happy Days" was Arthur Fonzarelli. This iconic character, often referred to as "The Fonz" or simply "Fonzie", was known for his leather jacket, motorcycle, and trademark thumbs-up gesture.
His popularity made him a cultural icon of the 1970s and 1980s. The show "Happy Days" itself takes the audience back to the 1950s and early 1960s, portraying an idealized vision of life in the mid-twentieth century America.