Germanic *xursa-/*xrussa- 'horse' has been linked by some Indo-Europeanists to Latin currō 'to run'1. This verb is derived from a Paleo-European lexeme *kərəs- also reflected in Celtic *karro- and Latin currus 'cart'2 < *kərəs-o-. However, in chronological terms, the traditional view of deriving 'horse' from a verb 'to run' would be like putting the cart before the horse. That is, the meaning 'horse' has to be older than 'run' and not the other way around.
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In my opinion, the Paleo-European word would be related to East Caucasian *ʁHwo:r[tʃʔ]o (˜ -tɕʔ-,-ə) 'deer, game', probably dating from the Upper Paleolithic. Possibly also Yeniseian *kuʔs 'horse' belongs here, as the names of domesticated animals are often Wanderwörter.
The Caucasian word is also the source of Kurganic IE *jorko-3 (Celtic *jorko- 'roe deer (Capreolus capreolus)', Greek zórks, dórkas 'gazelle'), with metathesis.
I also suspect this is the origin of the autochthnous name of the Pyrenean chamois (Rupicapra pyrenaica)4: Aragonese chizard(o), ixarzo, Gascon isar(t), idart, Catalan isard < *i-tsardV, with regular merger of sibilants /ts/ and /s/ in Gascon and Catalan and a prefix *i-, probably a fossilized article. There's also the unprefixed western variant *tsarri > Gascon sarri, Aragonés sarrio, the latter borrowed into Basque5.
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1 G. Kroonen (2013): Etymological Dictionary of Proto-Germanic, pp. 260-261.
2 Latin carrus is a Celtic (Gaulish) loanword.
3 Caucasian ʁ ~ Kurganic IE k and Caucasian tʃ ~ Kurganic IE j.
4 A species of mountain goat which lives in the Pyrenees, Cantabrian Mountains and the Apeninnes, considered to be a subspecies of the chamois (Rupicapra rupicapra) by some specialists.
5 The lack of a native Basque word for the animal can be explained from its absence from the Basque-speaking area.
