“Betty, some folks have left something dead lying around out here.” Joe spoke in the clicks, neighing and lip rumbles of the horse language. Betty could understand English, but she didn’t speak it very well. Joe also felt it only polite when they were having a private conversation to speak her language. Conversing in the horse language also provided them with privacy when unfriendly ears were around.

“Child, death is what usually draws us to our task,” Betty explained, always the teacher.

Joe looked over his right shoulder to their companions. To bring the peace the Paladins each traveled with a native Medicine Walker of the Woa-wah-nokt tribe. The Paladin Ranger Corps had been established to bring and enforce an uneasy truce

Impressions:
There’s not a strong hook yet, but you have more time in a novel. What you have here is good, it just needs some tweaking.

I like talking animals, I do. I prefer it to be more seamless though. This hits me between the eyes with “Hey, this horse can Talk!”
You could pare that down; you have an interesting take on the use of language, but maybe sprinkle it in more naturally as you go?
I am intrigued by the role of the horse as the wise one.

It’s interesting to have “reds” and others (“whites”?) working together, so I’m thinking early-America. The word Paladin Ranger makes me think of a medieval-fantasy world. Paladins and reds don’t quite go together in my mind. I think it would help to establish the setting a little more, to feel grounded in a place first, and then unfold the particulars of some individuals in this group, before bringing in the politics.

Nits:
I liked the possible implication of an inciting incident in the first line: “Betty, some folks have left something dead lying around out here.” But then it fell flat when you revealed that it’s commonplace, to be expected for this group. I formed an expectation that wasn't delivered.

Three references to “language”, two to “also” and “converse/conversation” and “private/privacy” in the first paragraph: watch out for repetition. The “horse language” doesn’t quite work for me, but I can’t explain why or give any suggestions *shrug*

The reference to “unfriendly ears” could be explained; how much danger is there? Should I worry for Betty and Joe? That could wait (but not too long).

“death is what usually draws us to our task” This doesn’t sound particularly pithy for a common soldier. So what is Joe’s role? What task?
Have you been introduced to beats? (for example: Betty tossed her head. “Go easy on the reins.”)
General advice around here is, avoid words that replace “said” (said is invisible; don't be afraid to use it).

I do not know if Joe is a Paladin, and if his companions consist of one medicine-walker and horse, or a larger group. Suggest being more specific: Harry, a Medicine Walker of the Woawahnokt tribe, paced along on his roan mare Fred. (Note: I removed the hyphens; they seem contrived.)

Suggestion: The Paladin Ranger Corps was established to impose peace between the native Pangaean “reds” and the non-red Terragaean. The Corps stayed busy enforcing the uneasy truce. Alternate: The Paladin Ranger Corps enforced an uneasy truce between the native Pangaean “reds” and the non-red Terragaean.