The arise of the Church of Christ in these last days, being one thousand eight hundred and thirty years since the coming of our Lord and Savior Jesus Christ in the flesh, it being regularly organized and established agreeable to the laws of our country, by the will and commandments of God, in the fourth month, and on the sixth day of the month which is called April— (D&C 20:1)
With this modern day revelation guiding Joseph Smith to officially organize The Church of Jesus Christ of Latter-day Saints the birthday of Jesus Christ was revealed to the world and established for Mormons. This has been reinforced by the comments of two subsequent prophets:
See Harold B. Lee in “Strengthen the Stakes of Zion,” Ensign, Jul 1973, 2:
This is the annual conference of the Church. April 6, 1973, is a particularly significant date because it commemorates not only the anniversary of the organization of The Church of Jesus Christ of Latter-day Saints in this dispensation, but also the anniversary of the birth of the Savior, our Lord and Master, Jesus Christ. Joseph Smith wrote this, preceding a revelation given at that same date:
“The rise of the Church of Christ in these last days, being one thousand eight hundred and thirty years since the coming of our Lord and Savior Jesus Christ in the flesh, it being regularly organized and established agreeable to the laws of our country, by the will and commandments of God, in the fourth month, and on the sixth day of the month which is called April.” ( D&C 20:1.)
Traditionally since that time, the spring conferences of the Church are held on the days of each year which include April 6.
See Spencer W. Kimball in April 1975 General Conference, Why Call Me Lord, Lord, and Do Not The Things Which I Say?:
The name Jesus Christ and what it represents has been plowed deep into the history of the world, never to be uprooted. Christ was born on the sixth of April. Being one of the sons of God and His Only Begotten, his birth is of supreme importance.(See also the Institute Manual for the Doctrine & Covenants)
Mormons appear to celebrate it on December 25 for no other reason that it is now tradition. There is compelling scholarly evidence that spring is the most accurate time for Christ's birth:
Consider the words of the following commentators:
From Dr. Richard O. Cowan in Q&A: Questions and Answers", New Era, Dec. 1974, 10–13:
The Book of Mormon bears a similar testimony. The Nephites dated their calendars from the time of Christ’s birth. (See 3 Ne. 2:8.) Then, the sign of Christ’s crucifixion was given “in the thirty and fourth year, in the first month, on the fourth day of the month.” (3 Ne. 8:5) This meant that Jesus Christ’s mortal life lasted almost exactly 33 years, and therefore his birth and crucifixion occurred in about the same season of the year. This would have been early spring because the New Testament indicates that Christ was crucified at Passover time, which falls in that part of the year.
Bible scholars generally agree that Jesus was not born in the winter.
“It could not … have fallen in January or December, since at this time of the year the flocks are not found in open fields during the night. … Moreover, a census which made traveling necessary, would not have been ordered at this season.”1Dr. Cowan also explains how the Savior's birth was simply merged with pagan beliefs:
Pope Gregory (A.D. 590–604) instructed these missionaries: “Remember not to interfere with any traditional belief or religious observance that can be harmonized with Christianity.”2 Such instructions opened the door to many pagan ideas and practices being introduced into Christianity. The observance of Christmas provides several examples.
December 25 was at the heart of the northern European mid-winter festival. There was a fearful superstition that as autumn days became shorter and shorter the sun might sometime completely disappear below the southern horizon and never return. Each year the coming of the winter solstice dispelled this fear, and the people rejoiced that the sun would again come back to warm their northern lands. Early Christian missionaries chose to link this important pagan celebration with the birth of Christ.There is evidence that Joseph Smith approved of celebrating Christ's birth at Christmas time.
From Roger A. Hendrix in "I Have a Question", Ensign, Dec. 1992, 28–30:
. . . Despite Puritan attempts to ban Christmas celebrations in early New England, Christmas in Joseph Smith’s day continued to evolve from a time of “folksy conviviality”1 into a religious event. Although Nauvoo school records indicate that Latter-day Saint children there in the early 1840s went to school on December 25, by midcentury Christmas in America and in Europe had taken on a deeper meaning.
For example, on 25 December 1843, the Prophet recorded that he had been awakened about 1:00 A.M. by carolers. The serenade of “heavenly music” caused him “a thrill of pleasure,” and he thanked God for the visit and “blessed them in the name of the Lord.”2 That evening, the Prophet enjoyed other festivities as well. His favorable response to Christmas celebrations suggests that he saw nothing objectionable about the holiday taking on religious significance.Our current prophet, President Thomas S. Monson, gave us this counsel in this season's First Presidency Christmas Devotional:
Brothers and sisters, this joyful season brings to all of us a measure of happiness that corresponds to the degree to which we have turned our minds, feelings, and actions to the Savior, whose birth we celebrate.
There is no better time than now, this very Christmas season, for all of us to rededicate ourselves to the principles taught by Jesus the Christ.Perhaps whatever refocuses our lives on Jesus Christ is good.
Update: The Deseret News on December 24, 2010 published "The real date of Jesus' birth" by Michael De Groote which upends some of what I posted above. It probably went live at the time I was composing my post although my post was published at 8 a.m. Christmas Day. See the BYU Studies article it references, "Dating the Birth of Christ" by Jeffrey R. Chadwick.