In my rural minded opinion and having lived around folks who used the expression "wrang it out" occasionally in conversation, the word has to do considering the answer to something and not figuring it out or trying to figure something out by thinking really hard, like continually putting a piece of wet laundry through a wringer attached to wash tub or a washing machine to get it as dry as possible so that it would only have to hang on the clothes line for a short time.
Wow, do I feel like an urbanized pervert.
I also assumed that the "wrang it out" phrase referred to Ennis, shall we say, reliving fond memories of Jack on the mountain -- especially since Annie uses this phrase along with the reference to Jack "riding more than bulls." Maybe Ennis was just thinking about whether he should or how he could contact Jack... can I have half a loaf and decide that he was using the phrase in both meanings?
Which reminds me ... in the motel, when Ennis says he almost gave up on hearing from Jack again, did anyone else want to scream to Ennis, "How many Twist families could there be in Lightening Flat, why didn't you contact his parents to find out where he was?" I guess Ennis was too scared to take responsibility for tracking Jack down.