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 *krs- also reflected in Celtic *karro- and Latin currus 'cart'2 < *krs-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.
In my opinion, the Paleo-European word would be related to Caucasian *ʁHwo:r[tʃʔ]o (˜ -tɕʔ-,-ə) 'deer, game', probably dating from the Upper Paleolithic. Possibly Yeniseian *kuʔs 'horse' also 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.
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.