However, I subsequently discovered that matters are a little more complicated. A number of commentaries discuss the question of how Avraham could have simply taken a sheep that might have belonged to somebody. Chizkuni, Seforno and Bechor Shor say that this is the meaning of the curious word אחר appearing in the phrase והנה איל אחר נאחז בסבך בקרניו. They explain that it means "subsequently." Avraham saw the ram roaming around, but did not take it, out of concern that it belonged to somebody; subsequently, when he saw it get trapped by its horns, he understood this odd occurrence as a sign that he should bring it as an offering. (See too Netziv, Haamek Davar, for a slight variation on this.)
R. Yisrael Lifschitz also addresses the ownership of the ram in his Tiferes Yisrael commentary to Mishnah Avos 5:6. The Mishnah there describes this ram as one of things created at the end of the week of Creation. R. Lifschitz states that this does not mean that Avraham's ram was created thousands of years earlier, but rather that his ram was a descendant of that primordial ram. He explains that this is in order to avoid the problem of Avraham taking somebody else's ram - it had to be a descendant of the primordial ram that had always been ownerless.
The common theme with all these commentaries is that none of them suggest that it was a wild ram (i.e.a mouflon), not a domestic ram! Why not?
Could it be that these commentaries were unaware of mouflons? Possibly, though that does not seem likely. I think that there are two other possible answers.
One is that perhaps the word ayil itself denotes a domestic ram. It is true that the English word ram is equally applicable to the males of wild sheep such as mouflons, but that does not need to be the case with the Hebrew word.
Another answer is that a mouflon is ruled out because a wild animal cannot be brought as on offering. Without getting into the ever-popular topic about whether the forefathers actually observed all the mitvos (a topic about which I am currently preparing an extensive analysis for the Rationalist Judaism book), we see that Noah only brought offerings from domestic animals, and thus this is a pre-Sinaitic concept.
In any case, is it actually possible for a ram to get trapped by its horns? Yes it is! Here is an incredible video of a mouflon actually trapped by its horns in a thicket, exactly as described in the Torah! (Note for those reading this post via email subscription - as usual, you will have to visit www.RationalistJudaism.com in order to see the video.)