Ibn ‘Umar used to pick his pebbles from Muzdalifah, and so did Sa’id bin Jubair. Ash-Shafi’i regards this preferable, but according to Ahmad one may pick pebbles from anywhere one wants.
‘Ata and Ibn Al-Munzhir hold a similar view, for in the hadith of Ibn ‘Abbas the words used by the Prophet (peace be upon him) are “pick (some pebbles) for me” without specifying the place whence these were to be picked.
According to the Hanafi and Shafi’i schools, and Ahmad it is permissible, though undesirable, to use pebbles that have been used before. Ibn Hazm holds it permissible without any dislike. He says, “Throwing the pebbles that are used before is permissible, and so is throwing pebbles while mounting an animal.”
Neither the Qur’an nor Sunnah forbids the use of used pebbles. Logically speaking, had those pebbles not been re-used by multiple pilgrims, there could have been mountains of them in the area.
As to throwing pebbles while riding one’s mount we read in the hadith of Qudamah bin Abdullah that he said, “On the Day of Sacrifice, I saw the Prophet (peace be upon him) throwing pebbles on the first Jamarah Al-Aqabah while he was riding a light-coloured she camel without throwing them hard or slow, nor pushing and shoving others.”