It is narrated from Imam Sha'bi (may Allah have mercy on him) that he met a horse rider and greeted him first with salam. (His student Husain says) I asked: Why did you greet him first? He replied: I saw Shurayh (may Allah have mercy on him) that even while walking on foot, he would initiate the salam.
Benefits and Issues: The Sunnah is that the rider should greet (give salam to) the one who is walking, and this is what should be practiced. However, if there is some benefit or necessity, it is also permissible to do the opposite.
Source: Fadlullah al-Ahad: Urdu Commentary on al-Adab al-Mufrad, Page: 997