Question: 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?

Answer: 
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](https://www.lds.org/topics/christmas?lang=eng). The current Church President, Thomas S. Monson, is quoted on the website:

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> 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.
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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.