In some part of the world, Shia people organize EID Salaat in mosques on the day of EID-Al-Ghadeer.
Is it valid to perform ID Salaat on EID-E-Ghadeer day?
Eid Ghadeer Khum is a Bid'ah, along eid Azahraa' and Al Mawlid Annabawi. All unknown to the Prophet's (peace and blessings be upon him) time, and Ali, Hasan and Husain, as well as the shabah and the Tabi'een, and the third best generation. The only Eids in Islam is Eidul Fitr, and Eidul Addha, along with Youmul Jumu'ah (يوم الجمعة). All Bid'at/innovations in Islam, will with absolutely no doubt lead to hell fire, and through innovations in religion Shaytaan gets to people.
كُلَّ مُحْدَثَةٍ بِدْعَةٌ وَكُلَّ بِدْعَةٍ ضَلاَلَةٌ وَكُلَّ ضَلاَلَةٍ فِي النَّارِ
every newly-invented thing is an innovation and every innovation is going astray, and every going astray is in the Fire
Islam was completed before the Prophet's death, anything new added would be Bid'ah, and the exceptions are Taraweeh for that is a matter of Fiqh, and the compilation of the Quran into one book for that was a necessity. Furthermore in celebrating these Eids which have been made up and are innovations, there is no good in them, and there will be no Thawab for those who celebrate them. So back to your question, there are no Salat on these eids for the Prophet never prescribed any, there are only the five daily Prayers just like any other day, if it is Jumu'ah then there is Jumu'ah prayer.
For further information, see this.
Eid salaat is to performed on Eid day only. There are only two Eid days in Islam. If you are praying on some other day, then is it to compensate for the one missed on Eid day? If it is, then, since Eid prayer is not "farz", there is no need to fulfill it. If you are prayer as "nafl", I don't see any problem, as you can pray as many on any day, either in congregation (as done during Ramadan) or individually.