It’s cold up north in Amarillo, but “There’s nothing between Amarillo and the North Pole except a barbed wire fence” is an exaggeration. The saying was considered old as early as the 1920s.
 
 
1 January 1922. Dallas Morning News, magazine section, pg. 1:
Amarillo climate has been much maligned, residents say. An old gag that “there’s nothing between Amarillo and the North Pole but a barbed wire fence” is no longer funny to people who live here, even when they are not at all interested in the real estate business. As a matter of fact, the average mean winter temperature is 43 degrees and the average mean summer temperature is 69 degrees.
     
23 June 1924, Dallas Morning News, part 2, pg. 10:
Indeed, some of them did not deny having favored the two days of quite warm weather in order that the old calumny might be disproved—the calumny that represented Amarillo as being the last station between the temperate zone and the North Pole, with only a dejected barb wire fence for a windbreak.
       
Google Books
I Give You Texas!
500 Jokes of the Lone Star State
by Boyce House
San Antonio: Naylor Company
1943
Pg. 8:
Away up on the plains in the Texas Panhandle is the city of Amarillo, 3,500 feet above sea-level. An old saying is: “There’s nothing between Amarillo and the North Pole except a barbed wire fence.”
 
And when it’s especially cold, say, around Austin, down in the middle of Texas, you are sure to hear the remark: “Somebody musta tore down Amarillo’s fence.”
 
It is said that when Admiral Peary reached the North Pole, he remarked: “Gee, I’ll bet it’s cold in Amarillo this morning.”
 
Google Books
Folk Travelers: Ballads, Tales and Talk
by Mody Coggin Boatright
Dallas: Southern Methodist University Press
1953
Pg. 200:
They have to be: between Amarillo and the North Pole there’s only a barbed wire fence with a single strand…and that’s down!