"Pulling calfs" refers to birthing calfs in a snow storm, sometimes the cowboys need to physically pull a calf out of its mother
Woolies = a kind of chaps made of angora goat skin with the wool still on the outside. Worn by only a few cowboys in the wintertime
Dogie = a young calf
Chinch is the strap that goes around the horse's belly to hold the saddle in place.
Chopping ice, this is neccessary to free up water for the cattle, who could not get to water under the ice.
Stetson is a brand of hat famous for western styles
"Daddy of 'em all" is slang for a rodeo
Wild galoot refers to a bucking bronco
"Rolling his own". Depending on your interpretation of the song, this could refer to how the bronco rider must rock forward and back to keep in time with the bronc to stay on its back for 8 seconds to qualify for the prize, or could refer to rolling his own cigarette

Cowboy, great American Cowboy -
Big high boots, Steston hat, and a lether vest
Cowboy, Great Amereican Cowboy -
With a hoss and a rope and a gun, he tamed the West!

Well, he's up at the crack of dawn, puttin' thoes woolies on
The wind's so cold the chills are runnin' down his back
The cattle range is froze, and every little dogie knows
He's an angel of mercy mounted on a horse's back

Cowboy, great American Cowboy -
Big high boots, Steston hat, and a lether vest
Cowboy, Great Amereican Cowboy -
With a hoss and a rope and a gun, he tamed the West!

Well, he's up at the crack of dawn, cinchin' that saddle on...
Stormin' hard and things are lookin'g mighty grim
There's a long ride ahead that day choppin' ice and a-feedin' hay
'Cause he knows every critter's life depends on him!

Cowboy, great American Cowboy -
Big high boots, Steston hat, and a lether vest
Cowboy, Great Amereican Cowboy -
With a hoss and a rope and a gun, he tamed the West!

Well, he's up at the crack of dawn, puttin' that bacon on...
Winter is past and the skies are clear and blue
There's springtime everywhere, and the dogies are a-frolikin' there...
And he's thankin' the Lord once more for a-seein' 'em through

Cowboy, great American Cowboy -
Big high boots, Steston hat, and a lether vest
Cowboy, Great Amereican Cowboy -
With a hoss and a rope and a gun, he tamed the West!

Well he's up at the crack of dawn puttin' that Stetson on...
Headin' for the "Daddy Of 'Em All" to celebrate
Well, he busts out of that chute, ridin' that wild galoot
Smilin' and a-rolin' his own as he counts to eight!

Cowboy, great American Cowboy -
Big high boots, Steston hat, and a lether vest
Cowboy, Great Amereican Cowboy -
With a hoss and a rope and a gun, he tamed the West!

With a hos and a rope and a gun, he tamed the West!
With a hos and a rope and a gun, he tamed the West!

Cowboy, Cowboy,
COWBOY, COWBOY!!!