Actually, the very word "Easter" comes from "Eostre" the Roman goddess of fertility. We get the words "estrus" "estrogen" and other words relating to female reproduction. Thus rabbits and eggs.
The fact that Jesus was resurrected around this time of year made it a great excuse to replace the pagan festivals of "Eostre" with a Christian celebration of the resurrection. However, there was already a pagan revelry around that time of year. The Church simply took it over.
As to the church having "authority" to establish a holiday, the Puritans in England would have disagreed. Under the regulative principle (i.e., you worship God how HE tells you to worship, and not just how it strikes your fancy), Christmas was banned for a short time under Cromwell. They would actually put you in jail if you closed your shop for Christmas! The church also excommunicated Martin Luther, banned Athanasius, burned Hus at the stake, censured Galileo and forced him to recant, killed multitudes of anabaptists, and performed a number of dodgy activities which are certainly not "established in heaven."
I love the church, but you are on VERY thin ice if you are attempting to extrapolate a pericope confirming the pattern and practice of Church Discipline (Mt 26) to a universal approbation of heaven on everything the church does in its official capacity as the church. There is just too much evidence that the official activities and pronouncements of the church in history are shot through with the sin Jesus died for to pretend otherwise.
But there's not much dispute regarding the date of Easter because it's pinpointed in the Gospels themselves -- we know it was right at the Passover. The Church had a good deal of debate regarding how to set the date of the Easter celebration, because of course Passover being based on the Jewish lunar calendar moves around with respect to both the old and modern Western calendars. But they did figure out a formula, it moves around a little (that's why it's called a "moveable feast") but it stays very close to the actual date. More than you wanted to know about how to calculate the date of Easter.
The date of Christmas is far more uncertain, but believe it or not it's in the ballpark. A list of dates for priestly service in the Temple was found among the Dead Sea Scrolls, and if you figure out when John the Baptist's father Zechariah served as a priest, you can calculate from there because we know from the Gospels that he was told of his son's conception while he was serving in the Temple, and that Elizabeth was six months pregnant when the Virgin Mary conceived. It works out to some time in December . . . obviously it's much fuzzier than the Passover date, but it wasn't just picked out of thin air as a pagan holiday.
(And A.Pole rightly observes that ANY day you pick will be on or near SOME pagan holiday -- they had a lot of them.)
This is a problem of English/Germanic languages. In Greek Easter is called Paskha (Pas'ha) from Hebrew Pesah, Pasover, in French Pâques, in Italian Pasqua.
The fact that Jesus was resurrected around this time of year made it a great excuse to replace the pagan festivals of "Eostre" with a Christian celebration of the resurrection.
Anglosaxons who worshiped Eostre became Christians much LATER than Greeks, Romans etc . And King James Bible is the not original Bible :) Trust me. As to the church having "authority" to establish a holiday, the Puritans in England would have disagreed.
Puritans were a sect which came into existence sixteen centuries after the Church was established by Jesus Christ. They were grew up withing the Church of England under the influence of Calvin.