According to Georges, the original meaning of Lat. cohors is 'a place that is fenced all around, the courtyard, the enclosure, especially for livestock, the stockyard'. Through metonymical transfer, such meanings as 'crowd, bevy, entourage' as well as the commonly known special military terms ('a tenth of a legion, bodyguard' etc.) arose. Within the Alpine region, the original meaning has been preserved ('open area for milking and sleeping around the Alpine hut'), while it also underwent a natural metonymical transfer to pasture huts (cf. the analogous polysemy of the base type malga).
Varro refers to two derivations of the word cohors he considers plausible: It could either be connected to the verb coorior and thus denote the place around which livestock gathers (according to R.G. Kent's translation [Varro. On the Latin Language, Volume I: Books 5-7. Translated by Roland G. Kent. Loeb Classical Library 333. Cambridge, MA: Harvard University Press, 1938], although this meaning is hard to bring in line with the other recorded meanings in Georges and, more generally, the basic meaning of the simplex oriri altogether), or it could be related to the Greek χόρτος, which itself seems to be linked to Lat. hortus (Varro, De Lingua Latina 5,88: cohors quae in villa, quod circa eum locum pecus cooreretur, tametsi cohortem in villa Hypsicrates dicit esse Graece χόρτον apud poetas dictam). Both hortus and χόρτος originally have quite similar meanings to cohors (on χόρτος see, e.g., Il. 11, 774 or 24, 640).