Rick Goldschmidt tells the story of the creation and restoration of the TV special Rudolph the Red Nose Reindeer in this TV Party article:

"Then came, what I consider the most significant deleted scene, which we called "The Peppermint scene." After Santa's sleigh takes off for the Island of Misfit toys being guided by Rudolph, we see several characters for the very last time in the special. Donner, Mrs. Donner and Clarice are all proud of RUDOLPH. As Rudolph flies away, Donner says "That's my Buck!" This confirms that he is no longer ashamed of his Red-nosed son.

Yukon comes running out of the castle and yells at his sled dogs (who wouldn't pull his sled throughout the special) "See! That's how it's done!" as he looks up at Rudolph. Then Yukon throws his pick up in the air and picks it up and licks it (As he did throughout the entire special).

His pick licking never made any sense. He thought he was looking for silver and gold, but he was really looking for Peppermint. After licking his pick, he says, "Peppermint! What I've been searching for! I've found me a peppermint mine....yahoooo!"