Jehovah's Witnesses believe there is no indication that Easter was celebrated in the first century by Christians. They say that reputable sources link Easter to false worship because there's no record of the Easter celebration in the New Testament. Watchtower Magazine, July 15, 2002, Article: 'They Keep On Walking in the Truth'
Because there is no mention of an Easter celebration in the Bible, the Witnesses postulate that early Christians did not celebrate Easter and it's not for Jehovah's people today.
What about the resurection of Jesus? Wouldn't that be an appropriate religious celebration for Christians? According to the Witnesses, Jesus commanded his disciples to commemorate his sacrificial death, not his birth or resurection. Romans 5:8; They say that the memorial of Christ's death or the 'Lord's Evening Meal' is the only celebration Jesus commanded his disciples to observe. Luke 22:19,20. This is the only religious celebration that is approved by the leadership of Jehovah's Witnesses. Celebrating other religious holidays is not allowed. See the 2010 Rules in the Elder's Manual
The April 1, 1996 Watchtower, discusses the reasons why Jehovah's Witnesess don't celebrate Easter. Here are the highlights of what they believe.
See Watchtower Magazine, April 1, 1996, Article: 'Easter or the Memorial—Which Should You Observe?';
The literature of Jehovah's Witnesses also associates Easter with ancient sex worship. It says that the celebration of Easter is an 'unclean thing' because it's roots are in pagan sex worship. Watchtower Magazine, March 15, 1968, Article: 'Easter—Relic of Ancient Sex Worship'
The Encyclopedia Britannica sys that 'The earliest recorded observance of an Easter celebration comes from the 2nd century, though the commemoration of Jesus’ Resurrection probably occurred earlier.' However the same article discusses the date of Easter and it's controversies.