How authentic are the two hadiths: "The horse has a quarter of what is permissible" and "Treat horses kindly"?

The hadiths mentioned in the question are not reported, but authentic hadiths have been reported regarding the virtue of horses, including: "Blessing is in the forelocks of horses," and "Goodness is tied to the forelocks of horses until the Day of Resurrection: reward and spoils." Al-Khattabi interpreted "goodness" here as wealth, citing Quranic verses.