Here is the very first Chilly Willy cartoon, entitled Chilly Willy. It is interesting to see how Chilly changes over the years. Chilly's appearance is different in this episode from later episodes.
From The Walter Lantz Encyclopedia:
Chilly Willy the penguin is one of the Walter Lantz studio's most recognized and beloved stars, and seemed to flourish in the late 50s, a period when most people feel the Lantz cartoons were in decline. In 1949, Walter Lantz retired his second biggest star, Andy Panda, leaving only one major character to star in his new cartoons: Woody Woodpecker.
In 1953, Lantz wanted a new character, and one of his directors, Paul Smith, began work on a cartoon entitled Chilly Willy. This cartoon features a little penguin, more similar in design to the ones found in 1945's Sliphorn King of Polaroo than the Chilly Willy we think of today, voiced by Sara Berner. This cartoon set up the general formula of Chilly wanting to find warmth that most future Chilly Willy cartoons would adhere to, and it introduced an early version of the familar Chilly Willy theme song.