I know little about horses. Did the Chinese think horses were arrogant? Why?
Above is Yellowbridge above. Below is Oxford Chinese Dictionary (2010) p 365.
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A horse might not directly represent 'arrogance', but status, wealth, power, elite, proudness, and unruliness are all potential cause of arrogance
Owning horses was a sign of wealth and power in the time most of the population were farmers
The number of horses you were allowed to use for a carriage indicated your status, No matter how wealthy you were, if you were not a noble, you could not have a four horses carriage and only the emperor could use a six horses carriage
Only Elite warriors ride horses
Wild horses are proud, unruly
Notice: 'proud' and 'arrogant' are very similar, differ mostly in degree of outward expression. 'proud' is more likely the original meaning of 骄 and 'arrogant' is a logical extension
Tl;dr: Simply put, yes (point 1.). But there are etymological uncertainties (points 2. and 3.).
The above is the Shuowen explanation for
驕: a six-feet horse. 'Sturdiness' (or 'strength', see
驕陽, 'scorching sun') and 'pride; arrogance' are probably derived from its impressive stature. (Shuowen also gives the explanation 'a wild horse'. Duan Yucai (段玉裁) from the Qing Dynasty thinks 'arrogance' arises from here:
一曰野馬。凡驕恣之義當是由此引伸。) At any rate, there is semantic extension from an equine adjective to a general adjective.
How credible is Shuowen? It gives the Shijing citation
我馬唯驕, but this is not found in existing versions of Shijing. We find
駒 in place of
驕 in Brilliant are the Flowers (皇皇者華):
維 here functions like a copula,1 suggesting syntactical equivalence between
我馬 ('my horse') and the characters containing the 馬-radical. It is therefore fairly certain that
駰 are types of horses, or equine adjectives. In fact, they mean 'young horse', 'piebald horse', 'white and black-maned horse', and 'gray horse' (trans. James Legge) respectively.
We are certain that
驕 should also be a type of horse, or an equine adjective; the only uncertainty is whether there is equivalence between
驕 (a six-feet horse) and
駒 (a young horse). Duan Yucai, with the help of two other Odes, argues the original character should be
驕, but it was changed to
駒 for the sake of rhyme (with
三詩義皆當作驕而俗人多改作駒者，以駒與蔞株濡諏爲韵。驕則非韵。). Logically, young horses can yet be ridden (
駒未可駕車。故三詩斷非用駒本義。); therefore Duan is a proponent of retaining
驕 in the verse.
I found this this, 骄 is simplied 驕.
A horse with six (ancient Chinese) feet hight is 骄 whose original meaning is "strong horse", gradually it was used to describe pride / arrogant or unruly related meanings.