Not true. Originally the Easter holiday celebrated rebirth/resurrection and the fertility of the land and all living things. It occurred around the Vernal Equinox when the days began to lengthen, which was considered the start of the agricultural year and a time for new beginnings.
Festivals of springtime date back to 2,000 BC in the Middle East which celebrated the resurrection of the gods and goddesses, Osiris (Egyptian) and Ishtar/Inanna ( in Babylon & Sumer). Easy to see how it seemed a logical time to celebrate the resurrection of Jesus.
Pagans in the Saxon countries celebrated the return of spring each year with Easter festivals honoring the Goddess of Dawn named Eastre,Oestre, or Ostara, depending on the region. She was the goddess who was responsible for bringing springtime (fertility and renewal) to the land each year. (We get the word for the female sex hormone estrogen from her name, btw.)
One year the German goddess Ostara arrived late and discovered a small bird whose wings had frozen during the lengthy winter. Feeling guilty that he would surely die since he could no longer fly, she turned him into a hare. And she also gave him the ability to lay eggs as a reminder of his earlier life as a bird. And the eggs would be in every color in the rainbow, no less!
There's a lot more to the story of the Easter Bunny as well as the origin of other Easter traditions (including the dark reason why we "hide" the Easter eggs) at the goddessgift.com site I've referenced below.
Source(s):
http://www.goddessgift.com/pandora's_box/easter-history.htm