Somehow, I figured it out the first time I read it. From context, I guess, like "puttin' the blocks to," and "stemmin the rose."
What had puzzled me wasn't so much the meaning of the words but rather, What was the deal with a kid riding a sheep? The scene in
The Cowboy Way looks like it's some kind of race for little kids, like it's supposed to be a little kid's first rodeo event. So in this light, it seems to me that Jack might be saying that his father had gotten him started in rodeoing by putting him in one of these kids' events, and then never followed through with teaching Jack anything about rodeoing--kind of interesting in light of John Twist's snide remark about Jack's plans never coming to anything. Also, I'm guessing now Jack didn't mean his father just put him on the back of sheep to ride around the home spread. It's actually a rodeo-type event for kids.
Another
Brokeback resonance in
The Cowboy Way: Sonny, Keifer Sutherland's character, had an unresolved issue with Pepper, Woody Harrelson's character, because Pepper had failed to show up for a national championship team calf-roping event that they were supposed to enter, thereby preventing Sonny from winning the money he needed to set up the little cow and calf operation he had dreamed of since childhood.
Oh, yes, their event was calf-roping, so in my mind I kept hearing the bartender say to Jack, "Ever try calf-ropin'?"
Slightly OT: I also recognized Alison Janney, later/late of
The West Wing, in a small role as a police officer.
Katie77, my folks here in Pennsylvania, USA, also used the term "winter woolies"--to mean old-fashioned woolen long underwear.