Latin origin was originally dismissed quoting Century Dictionary and Cyclopedia of 1911, which says "common derivation from Armenia, as if mus Armenius, (...) is without any foundation", and postulates Old High German 'harmin/harmo' as the origin of French hermine and then English ermine. However, while there is indeed no documented mention to the Latin expression 'mus Armenius' explicitly, there are solid academic references to justify this hypothesis through Romance languages (Littré, Meyer, or Corominas).
Corominas in particular presents many convincing points:
While there are ermines in Central Europe, there's documented evidence of maritime imports of fur into Spain through Catalonia (recorded as 'armini')
Romance derivation (Old French hermine, Old Occitan ermeni, Catalan ermini) favours armenius over harmin, which would have then presented the ending -inus instead.
The initial e is present in Old French Ermenie ("Armenia"), Old Catalan ermini and Italian ermellino ("Armenian").
Spanish 12th century texts mention 'piel hermiña', 'manto erminyo' ("ermine fur", "ermine cloak"), while armiño (Spanish for "ermine") was used as a synonym of "Armenian" until at least the 14th century. Catalan used armeni/ermini indistinctively (nowadays ermini for "ermine" and armeni for "Armenian"). Italian for "ermine" still presents both ermellino and armellino.
Thus while it is not clear if 'musPonticus' ("mouse of the Black Sea") actually referred to ermines or even if the term musarmenius was ever used, the link between Armenia and ermine from Latin is widely documented.
Personally I feel more inclined to support the Romance path but this is not the place for critical analysis and some references such as Walter W. Skeat or OED often include both etymologies, so I've simply removed the citation of Century Dictionary and Cyclopedia to avoid any contradictions and presented both instead.
