The second route: Muslim ibn Ibrāhīm narrated it from Saʿīd ibn Muḥammad al-Zuhrī (one manuscript reads: al-Jawharī), from Ibn al-Musayyab, from Abū Hurayrah, from the Prophet ﷺ. Al-Bayhaqī cites it in this suspended form. All of these transmitters are trustworthy narrators found in the six canonical collections, save Saʿīd ibn Muḥammad—whether he be al-Zuhrī or al-Jawharī—for I have not located a biographical entry for him.
The third route: Ibrāhīm ibn ʿUyaynah said, “I heard Abū Ḥayyān report from Abū Zurʿah that Ibn ʿAmr ibn Jarīr related from Abū Hurayrah, attributing it to the Prophet with the wording: ‘Sheep are among the livestock of Paradise, so wipe the dust from their noses and pray in their folds.’” Al-Bayhaqī recorded it.
This chain, too, is ḥasan; its transmitters are reliable except for Ibrāhīm ibn ʿUyaynah, who is truthful yet prone to error, as stated in al-Taqrīb. Moreover, the narrator who reports this tradition from him—Sakhtawīh ibn Māzyār—has no biographical entry that I could find.
Al-Haythamī reproduces the ḥadīth in al-Majmaʿ with the wording: “The Messenger of Allah ﷺ was asked about praying in sheepfolds. He replied, ‘Wipe away their nasal dust and pray in their pens, for they are among the beasts of Paradise.’” Al-Bazzār transmitted it, and its chain contains ʿAbd Allāh ibn Jaʿfar ibn Najīḥ, who is weak. Aḥmad ibn ʿAdī said, “His narrations are written down but not taken as evidence.”