Muslims have only two Holy days to celebrate. The two Holy days are Eid Alfitir, which follows the holy month of Ramadan, and Eid Aladha, which is in the Hajj (holy pilgrimage) season. Muslims celebrate Eid Aladha by slaughtering a sheep. The slaughtering of sheep is done in following the footsteps of Prophet Abraham when he was ordered by Allah (God) to slaughter his first child, Ishmael. When he told his son about it, his son told him to carry on with the order of Allah, and that he will be obedient and patient. As Abraham was tempting to slaughter Ishmael, Allah gave them a big and fat sheep to slaughter instead. The sacrificing of a sheep has become a ritual for Muslims every year in remembrance of the obedience of Abraham and Ishmael, peace be upon them. Our celebration of this day and the slaughtering of the sheep are in compliance with the teachings of our Prophet Mohammad, praising and peace of Allah be upon him. Only Muslims celebrate these two days, while at the same time, Muslims do not celebrate the Christian holidays.
As for the symbol, Muslims worship Allah (God), therefor they reject any kind of idol worshipping. We believe that Christians believe in the cross to be a symbol of their God, or the so claimed Son of God. They seek blessing and protection from this cross. Muslims seek protection and blessing only from Allah, that is why we do not have an Islamic symbol as the Christians cross. Some Muslims have invented the symbol of a crescent to counter the cross, but this is not authentic and it is considered as an innovation in Islam.