No doubt celebrating such feasts is actually imitating disbelievers. The companion of the Prophet Abdullaah Ibn Amr Ibn al-'Aas, may Allaah be pleased with him, said: "Whoever celebrates the Persian New Year's Day or their carnival and imitates them till his death he will be resurrected with them on the Day of Judgment." The Prophet, sallallaahu alayhi wa sallam, said: "Whoever imitates a nation is but one of them." [Abu Daawood]
Fasting on the day of christmas has no connection with Islam. Neither does this islamic month of we muslims, i.e Muharram, has any importance of fasting on 25th of Dec.