The morpho-lexical type muaglia, which is particularly widespread in Grisons and neighbouring Lombardy, denotes either the individual cow or the herd of cows, whereby, for example, the existence of a "Societad d'allevamaint da muaglia bovina" in Celerina/Schlarigna (near St. Moritz) indicates that this does not specifically mean a HERD OF COWS, but a (FARM) ANIMAL HERD in general.
The fact that muaglia denotes not only the individual, but also the collective, and furthermore not only the *COW*HERD, rules out a connection with Latin mulgēre, MELKEN. Rather, a connection with Latin mōbilia (n. pl.) has been established (FEW6, 3: 1 under mobilis]) which seems plausible. The term thus refers to the mobility of the livestock and should be understood as a complement to the immovable property. The word muvel (m.) (roa.) found in the Lower Engadine, which designates the LIVESTOCK, can also be traced back to Latin mōbilis (FEW loc. cit.).

Wartburg, Walter (1922-1967): Französisches etymologisches Wörterbuch. Eine Darstellung des galloromanischen Sprachschatzes , Basel, vol. 20, Zbinden

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