"A Visit From St. Nicholas," by Clement Clarke Moore, is also known to many as "'Twas the Night Before Christmas." Published in 1823, it has become a holiday standard, read to children on Christmas Eve in preparation of Santa's visit. The poem is written in couplets, with a rhyme scheme of aa bb, etc. Several literary devices are employed. In this example, personification is used.
Personification is a form of figurative language whereby human characteristics are given to non-human things. For example, personification is used to describe leaves that "skip" down a road or daffodils "raising their heads" to the sun. This device provides a clearer mental image of the item being described, and is a device very often used in poetry. In the following example from "A Visit From St. Nicholas," the moon and snow are being discussed.
The moon on the breast of the new-fallen snow
Gave the lustre of mid-day to objects below...
In order to understand what is being personified, it is best to try to put the quotation into standard, modern English to better understand the meaning of the line. I.e., we need to understand what is being said before we can be sure what is being given human characteristics. The lines shown above state that the moon is reflecting off of the newly fallen snow, creating an illusion that the items below have a luster or shine from that reflection. Having done this, we can more easily ascertain what is being personified. This centers around one question: what does "breast" applies to—the moon or the snow?
Looking at the quote within the context of the entire statement, we find that "the breast" refers to "the snow," with the use of the word "of." We could translate the line to read:
The moon [shining] on the breast of the new-fallen snow...
The description does not refer to the breast of the moon, but the breast of the new snow, from which the glow or luster below comes. So your answer is that snow is being personified here.