All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is evidence from the Book of Allaah and the Sunnah of the Prophet that it is forbidden for a Muslim to glorify a day that is glorified by the non-Muslims or glorify a place where they gather for religious rites. All Muslims are commanded not to participate at a time or in a place that is glorified by non-Muslims. Abu Daawood reported that a man vowed to slaughter a camel at "Buwaanah", so the Prophet asked him: "Did this place ever contain any idol worshipped in pre-Islamic times?" He replied: "No." The Prophet again asked: "Did this place ever contain any idol worshipped in pre-Islamic times?" The man replied: "No." Thereupon, the Prophet ordered him to fulfil his vow.
There is no doubt that what is mentioned in the question, which is throwing colours and the like during the day of a Hindu religious celebration is considered as participating with them in their festival. Even if it is done without having the intention of participating with them, when one does so, he is imitating them. The Prophet said: "Whoever imitates a people he is one of them." [Ahmad and Abu Daawood] In addition to this, playing with throwing colours is a kind of extravagancy and harming people, and we are forbidden from being extravagant or harming people. Therefore, one has to be very cautious about this and a Muslim should be proud of his religion and belief, and not be dragged towards the celebrations of the non-Muslims and imitating them at a time they are openly showing their enmity to the Muslims.
To conclude, it is not permissible to do what is mentioned in the question as this is a kind of partaking in their religious celebrations and imitation of them. Please refer to Fatwa: 88293 about the relationship of a Muslim with a non-Muslim, and Fatwa: 83628 about the ruling of Muslims participating with non-Muslims in their religious celebrations.
Allaah knows best.