It is not permissible to take part in festivals originated or influenced by polytheism. Muslims should revive the sunna of the Prophet and celebrate Islamic festivals that have been sanctioned for the Umma like Eid al-Adha and Eid al-Fitr and understanding their scope without going beyond it. It has also been said that the Holi festival could be considered a "neutral" festival in relation to the coming of the spring like the Persian Nowruz. This is not something proven; rather what is proven is the fact that such festivals are not part of the established sunna but often mixed with polytheistic/pagan elements and therefore should be avoided by Muslims.
With prayers for your success.