Being a denomination which prides itself of the restored beliefs of the original church before false doctrine infiltrated the truth, do Mormons celebrate Christmas on/or around the 25th of December? If so on what scriptural basis do they have for that date?
Yes, Mormons generally celebrate the birth of Christ on the traditional day of Christmas, December 25. They never said there was scriptural basis for this date; the specific day of the year is not important to them.
As an addition to Matt's correct answer, to see how LDS Church leaders talk about Christmas one can visit "Christmas" under the Gospel Topics on www.lds.org. The current Church President, Thomas S. Monson, is quoted on the website:
When we keep the spirit of Christmas, we keep the Spirit of Christ, for the Christmas spirit is the Christ Spirit. It will block out all the distractions around us which can diminish Christmas and swallow up its true meaning.
This quote is taken from the 2011 First Presidency Christmas Devotional. The First Presidency Christmas Devotional takes place every year (usually on the first Sunday of December).
The website I linked above also has links to several other Christmas-themed talks from LDS Church leaders.
To add some additional context, Christmas was created after quite a few of the other Saints had their Feast Days cannonized by some of the early churches. Some time between the 2nd and 3rd century AD, it was determined that a feast day should be set apart for the Christ—literally "Christ's Mass." There is a lot of debate about the specifics for the date chosen, but it is generally accepted that the celebration of light coming back to the world during the Winter Solstice seemed a fitting time to celebrate Jesus as the "Light of the World."
Just as Antiochus IV Epiphanes choose this time of year to sacrifice to his gods, the Maccabees chose the solstice to rededicate the temple to God.
Within my own family, I enjoy celebrating many of the traditions that help my children focus on Jesus the Christ. We focus on St. Nicholas on his day (Dec. 6th), we talk about Hanukkah and the importance of the temple (though we do not celebrate the holiday per se), we try to focus on Jesus during his days (Dec. 24–25), we talk about the importance of boxing day/St Stephen's day (Dec. 26) and sing of Wenceslaus I, Duke of Bohemia, we also talk of the Wise Men on their day (Jan. 6th). I have never gotten into the habit of celebrating the Sundays of Advent (or the Holy Weeks leading up to Easter for that matter), but I believe they are worthwhile observances insofar as they point people to Christ.
The scriptural basis for me is in Philippians 1:18 and 2 Nephi 25:26. The specific day or days to rejoice in Christ should be less important than making sure that we do rejoice in He who is Mighty to Save.
That being said, many members also celebrate Jesus' birth on April 6th due to the wording in Doctrine and Covenants 20:1.
In this same vein, members of the Church of Jesus Christ of Latter-day Saints also celebrate Easter for the same reasons.