Howdy (“Howdy, Pardner!”)

“Howdy” is simply from “How do you?” and dates to back well before the Texas became independent from Mexico.
 
“Old Howdy” or William Harrison Martin (1822-1898) was a Texas Congressman who said “Howdy!” so much that it became part of his name. He fought with General Robert E. Lee in the Civil War and allegedly first greeted General Lee with a “Howdy!”
 
Howdy Partner was the title of a 1920 silent film by the author of the “Gumps” comic strip (ChicagoTribune). The westernism is often written as pronounced, as “Howdy pardner” or “Howdy podner.”
   
   
Internet Movie Database
Howdy Partner (1920)
Directed by:
Wallace A. Carlson
Writing credits:
Sidney Smith (comic strip The Gumps)
   
Rootsweb.com
William Harrison Martin
b. 2 September 1822, d. 5 February 1898
(...)
William Harrison Martin nickname was “Howdy”. It seems that he got this nick-name during the Civil War because, by way of greeting, he always said, “Howdy.” An interesting story that may be apocraphal, but still makes a good story, is that when General Lee came to inspect the troops, William Martin, instead of saluting, tipped his hat and said, “Howdy, General.”
           
(Oxford English Dictionary)
how-do-ye, how-d’ye, howdy, phr. and n.
Now obs. or dial.
The phrase how do ye? how do you? (cf. next) = how are you? how fare you?: see DO v. 19. Freq. in colloq. phr. to tell (a person) howdy.
1563-87 How do you? [see DO v. 19]. c1828 T. O. LARKIN in Calif. Hist. Soc. Q. (1937) XVI. 25 They (Southerners) often correct Yankees in their speaking… In those words they are right, but not in..how de for how do you do. 1837 A. WETMORE Gaz. Missouri 287 With a smile of welcome as she gave her hand, said, ‘Howdy, Joseph.’ 1850 J. PRICE Let. 17 Apr. in Mississippi Valley Hist. Rev. (1924) XI. 241 Tell Mother and the doctor Howdy.
       
13 April 1844, Milwaukie (WI) Sentinel, pg. 2, col. 1:
“Howdy, Major, howdy,” sez old Mr. Beers,...
   
25 August 1865, Coshocton (OH) Age, pg. 2, col. 4:
A hurried call upon a few old friends—a howdy and good bye to Cowles,—...
 
25 October 1865, Wellsboro (PA) Agitator, pg. 1, col. 6:
P.S.—Say “howdy do” to George Carter, and thank him for taking the pistol from you when you were shooting at me.
   
17 June 1878, Fort Wayne (IN) Daily Sentinel, pg. 4, col. 7: 
“Howdy, howdy, howdy do?
How is your wife, and how are you?
Ah! It fits my fist as no other can
The horny fist of the workingman.”
   
7 September 1886, San Antonio Express, pg. 4, col. 3:
“NOW HERE’S A HOWDY DO.”
The Seizure of Those Vessels Being
Investigated
 
7 February 1898, Washington Post, pg. 3:
EX-CONGRESSMAN MARTIN DEAD.
Known as “Old Howdy,” and Once Blew
Out the Gas in Washington.
Houston, Tex., Feb. 6—Ex-Congressman William H. Martin died near Hillsboro yesterday of pneumonia.
(...)
Mr. Martin was known to his constituents by the affectionate name of “Old Howdy.” He created a sensation in Washington, where he was regarded as a typical Western character. He promised, before he left home, that the life of the Capital should not change him, and he intended to cling to the butternut shirt and wide-brimmed sombrero of a ranchman.
 
6 March 1898, Washington Post, pg. 18:
Such was Old Howdy—a man among men; free from deceit and guile; a true friend; carrying a heart as big as the heart of an ox; a genial companion and associate; a sympathetic as a woman; as brave as a lion in battle, yet as kind-hearted a man as ever breathed. It will be long before his fame dies out in Congress, and in time to come, as he meets his old colleagues on the threshold of another world, his cheering salutation of “Howdy” will hardly be forgotten.
   
29 May 1920, Gastonia (NC) Daily Gazette, pg. 8, col. 2:
Howdy Do, My Partner, by First Grade Pupils.
 
17 February 1922, Mansfield (OH) News, pg. 12 ad:
THE FAMOUS GUMPS COMEDY
“HOWDY PARTNER”
(Silent film—ed.)
   
21 January 1939, Modesto (CA) Bee and News-Herald, comics section:
“HOWDY, PARDNER! WHERE ARE YOUR CHAPS AND SHOOTIN’ IRONS?”
   
8 October 1945, Galveston (TX) Daily News, “Kiwanis ‘Howdy Podner’ Roundup Ends First Day,” pg. 1, col. 6:
“Howdy, podner! Mighty glad you came!”