According to Gamkrelidze-Ivanov1, Celtic *marko- 'horse' (Old Irish marc, Middle Welsh march, Gaulish márkan [acc.])2 and Germanic *márxa-/*margá- 'horse, mare' (Old Icelandic marr 'horse', merr 'mare', Old High German marah- 'horse', meriha 'mare') is an Asian Wanderwort related to horseback riding in the Eurasian steppes before the first millenium BC.
The closest forms would be Sinitic *mrāʔ and Tibeto-Burman *mrāŋ 'horse', with Schwebeablaut. These words3 look as different formations from a lexeme found in Altaic *mórV 'horse' (Mongolian *mori, Tungusic *murin, Korean *màr). One of these derivations, with a nasal suffix (*mori-n), found in Mongol and Tungusic, would be the origin of the Tibeto-Burman word as well as North Caucasian *far-nē 'horse, mare'. The other would be a diminutive *mor-qa reflected in the Sinitic and Celto-Germanic words.
However, Sanskrit mṛga 'deer, antelope' would point to a possible origin of this Wanderwort in the domestication of wild horses by the Botai culture of northern Kazakhstan (3,500-3,000 BCE).
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1 T. Gamkrelidze & V. Ivanov (1995): Indo-European and the Indo-Europeans, p. 472-473.
2 R. Matasović (2009): Etymological Dictionary of Proto-Celtic, p. 257.
3 For which Sergei Starostin reconstructs a Sino-Tibetan protoform *mrāH / *mrāŋ.
