Some articles online, such as this Iranica Encyclopedia article, claim that hadith were influenced by Iranian ideas and practices. Such as Prophet’s prohibition on being despondent and gloomy at someone’s loss, the Prophet’s prohibition on urinating while standing, encouraging the use of sewak or meswak which may have originated from sawaag a Persian word for the same thing. The usage of odd numbers such as 3, 7 or 33 when mentioning the amount of dhikr, the number of rakaats (prayer rounds) or multiplying of deeds etc. The Prophet’s mount for Mir’aj called Buraq may be Arabicized form of baraag or baarag “a riding beast, mount” in Persian language, and his Mi’raj is the similar experience as recorded in Book of Arda Wiraz by a Persian Prophet or religious figure named Wiraz. It is also claimed that the Prophet ï·º must have adopted many traditions from his Persian companion named Salman Al Farsi (the Persian).

Prophet Muhammad ï·º never prohibited being gloomy, what he prohibited was wailing, a pre-Islamic ignorant act among Arabs was wailing and beating when in grief: “beware of the devil’s croaking! As long as it comes from the eye and the heart, it is coming from mercy; and as long as it comes from the tongue and the hand, it is coming from Satan.” (Narrated from Ibn `Abbas by al-Bayhaqi in al-Sunan al-Kubra) The Prophet ï·º prohibited his Ummah to urinate while standing but he also urinated in a very unclean place standing which made sense to avoid dirtying his clothes. (Sahih al-Bukhari 2471) The meswak or sewak, tooth stick introduced by the Prophet ï·º cannot be the Persian use of sawag because the use of meswak led towards a victory of Muslims in the battle against the Persian army. The book, Healing Body & Soul by Amira Ayad tells that Saad bin Abi Waqas (r.a), the army general and victor against Persian battles noticed that the Muslims were being defeated continuously. After evaluation he concluded that the Muslims had forgotten the Sunnah of meswak. He immediately ordered the Muslims to use meswak and ask Allah ï·» for forgiveness. The Persian spies in the Muslim camps saw the entire army using meswak thought that they were sharpening their teeth for cannibalism which spread fear among the Persians and they were routed. This shows meswak may not have been a Persian tradition. As for the usage of odd numbers like 3, 7 or 33, the Prophet Muhammad ï·º stressed this fact because the Quran stresses on this fact: (Al Quran 89:1) “By the dawn and the even and the odd.” The even is the creation and the odd is Allah ï·» because every even number is divisible such as 2, 4, 6, 8, but every odd is indivisible such as 1, 3, 5, 7, the even is creation that has pairs and opposites while Allah ï·» is unique and without pairs. This is not a Persian tradition I believe, its a philosophy of the Quran about Allah ï·» and His creation. As for barag in Persian that means “a riding beast or mount” cannot be equivalent to Buraq in Arabic because this term was not in use among Arabs for any riding beast. Prophet Muhammad ï·º used this term for the supernatural conveyance. Buraq was a special animal of a special kind because buraq is derivative of root barq which means “intense” and “bright lightning” while Persian term does not carry the same meaning. On the other hand the Persian literature called Book of Arda Wiraz where Wiraz, supposedly a Persian Prophet, gave details of his dream journey where he saw insight in to hell, paradise and communicated with Ahura Mazda (Allah). The book is actually compiled in 9th and 10th Century CE during Islamic period, hence it could possibly have been influenced by traditions of Mir’aj. But even if this dream journey was authentic and pre-Islamic then Prophet’s of Allah ï·» have received divine insight in to hell, paradise, day of judgment etc. But if one notices the details of the Mir’aj they conform to a physical journey experience than a dream, Prophet Muhammad ï·º had never traveled to Jerusalem, yet, to the amazement of disbelievers, gave the correct details of city, traveling caravans and places in between. In fact even in our times many recent scientific & astronomical findings explain the Prophet’s Mir’aj as well, please read the following writing:
Additionally there may be some misconception among certain Western academia, or others who hold the belief that the Salaah (5 times prayers) comes from pre-Islamic Persian tradition. What many forget is that initially prayers in Islam were 50 and were reduced to 5. At one point they were only 2, then increased to 5. As for Salman Farsi (r.a), he converted to Islam at the blessed hands of Prophet Muhammad ï·º during his prophet hood in the city of Madinah. Salman (r.a) was not present during first 13 years of the Prophet's mission in Makkah and this can be confirmed from all historical sources that mention the story of Salman (r.a) such as Salman the Persian. In fact during the Prophet's mission in Makkah there was no Persians that resided in the town and there was no influence of Zoroastrianism whatsoever.

References:
2. Ayad, Amira, and Jamila Hakam. Healing Body & Soul: Your Guide to Holistic Wellbeing following Islamic Teachings. pgs. 443-44
3. Isra Wa’al Mir’aj ​– Prophet’s Night Journey & Ascension
5. Pic taken from ​https://www.ames.cam.ac.uk/12th-century-fatimid-tiraz

[Courtesy of  Zaid Shah | Rizqan Kareem | Most Excellent Sustenance]