Yes, according to the RAE dictionary, the use of ora with this meaning has its origin as a shortened form of ahora:
1. conj. distrib. ahora. Tomando ora la espada, ora la pluma.
So, it replaces ahora only with a specific meaning: when it's used as a conjunción distributiva. Note that this is a rather archaic use, so you'll probably find it only in old or literary writings.
One problem that remains is that this type of conjunctions normally have to appear in pairs, but in this sentence there is only one ora. Where is the other one? Let's take a look at the complete sentence:
Ora enseñando los blancos dientes o dilatando las narices, ya enarcando el cuello o dando una corveta, compele a su grey y la lleva al trazo de gramilla; se para de súbito, arroja un pequeño gruñido felino, y se pone a pastar.
Here the author is mixing ora with ya, which is another conjunción distributiva. It would have been more standard to say:
Ora enseñando [...], ora enarcando [...]
Ya enseñando [...], ya enarcando [...]
In English, now can be used in a similar fashion. Although not all dictionaries list this meaning, I found it in Merrian Webster:
4: SOMETIMES now one and now another
now ——, now ——
At one moment ——, at the next ——:
a wind whipped about the house, now this way, now that
In summary: it is a shortened version of ahora, but only with a specific meaning, and it is nowadays almost never used except in poetry and literature.
Also, as the other answer mentions, ora can also be the present tense, third-person singular, of orar. It's not the meaning it has in this sentence, but keep it in mind if you find this same word again.