This is another one of those seemingly simple “yes/no” questions about Quakers that we actually have to answer “sometimes” or “it depends.”
From a theological standpoint, Quakers don’t buy into the notion of religious holidays; every day is a “holy day,” and every day is a good day to remember the Good News heralded by Jesus’ birth, his ministry, and his crucifixion and resurrection—assuming, that is, you’re working from a Christian mindset. (Some Quakers don’t!)
In that sense, then, Quakers don’t “celebrate” Christmas or Easter. As a practical matter, however, Friends live in the same world as everybody else, and we all know how much “the spirit of Christmas” permeates public culture at the end of the year, even if it often feels like a secular holiday that pays lip service to its religious roots. Although there might be considerable debate about whether to put up a tree in the meetinghouse, many Quakers do exchange presents with friends and family on Christmas, and though hymns are rarely heard in unprogrammed Quaker meetings, some Friends might be inclined to stick around after silent worship for a carol singalong, and it’s quite likely that during worship someone would share a message attuned to the spiritual themes of Advent or Christmas.
Easter may be less overwhelming than Christmas in the world at large, but it’s a very intense time in the Christian liturgical calendar. Less so for Quakers: Few if any Friends give up anything for Lent, we don’t do a Palm Sunday processional, and we don’t have any of the other church services that take place in Catholic or Protestant communities through Holy Week on to Easter Sunday. Of course, Friends probably know when Easter is approaching, and if they’re of a Christian persuasion they’re likely to have Jesus on their mind, so again you might very well hear an Easter message in meeting. (A meeting with a significant number of children might hold an Easter egg hunt, or it might not; it would all depend on what the adults decided.)
In short, Quakers may not make a big deal out of Christmas or Easter, but they also don’t act as if either holiday doesn’t exist.