The Puritans did not celebrate any scheduled holidays like Christmas or Easter. However, on any day when God favored them with good things, they were allowed to celebrate either of these special days:
Let’s look at the beliefs of the Puritans and see why they did not celebrate holidays.

The Puritans were not against secular holidays, like Thanksgiving. It was only the religious ones with the Pagan origins or influences which they objected to. It is interesting to note that:
The reason the Puritans did not celebrate holidays like Easter and Christmas was because of the fact that they came from Pagan ideas. As Christianity spread during the early years, church officials would make compromises to convert Pagans. One of these was combining the Pagan Saturnalia festival with the celebration of Christ’s birth.
For Puritans, their religion was their life. It was the foundation and played a big part of every facet of their society. Their religion had its roots in Calvinistic Protestantism and Puritans wanted to purify the church and themselves.
They were exclusive with their beliefs, meaning a non-Puritan could not live in their society. That way, in each town, everyone had the same goals and values. It also made for a town that was bonded together.
Puritan society was a theocracy, where God was the supreme ruler and government officials were divinely guided. Puritans were avid persecutors of Quakers, along with other colonies. They took religious intolerance to a whole new level in 1660. Mary Dyer, who was a Quaker, broke the law banning Quakers from the colony and was hanged along with three others. They were called the Boston Martyrs.
These actions set many things in motion starting with these three actions by King Charles II:
In 1689, the Toleration Act was passed. This was the end of the Puritan theocracy.