All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is not permitted for this woman or any other Muslim to participate in the festivals of non-Muslims because it is a kind of cooperation in the disobedience of Allah. Allah Says (what means): {…Help you one another in Al-Birr and At-Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression….} [Quran 5:2]. The Prophet said: “Whoever imitates a nation is but one of them.” [Abu Dawood] Celebrating such festivals comes under the falsehood that should be avoided. Allah Says (what means): {And those who do not bear witness to falsehood, and if they pass by some evil play or evil talk, they pass by it with dignity.} [Quran 25:72]. Many scholars of Quran like Ibn Seereen and Mujaahid interpret “falsehood” as the festivals of non-Muslims. Anas reported: “The Prophet came to Madeenah while they had two days they celebrated. The Prophet asked, “What are these two days?” They said, ‘These are two days we used to celebrate in our pre Islaamic era. The Prophet said: “Allah has replaced them with two better days: 'Eed Al-Adh-Haa and 'Eed Al- Fitr.”
Therefore, no Muslim is allowed to participate in the festival celebration of non-Muslims or greet them on this occasion. Imam Ibn Al-Qayyim reported the consensus of all scholars that greeting non-Muslims on their religious occasions is forbidden. Know that partially participating in such occasions is enough to involve one in sin even if one does not intend to participate wholly in the celebration.
Allah knows best.