There is an art, of course, to writing hymns. The composer can't just say what they want—the metrical restraints of the stanza lines require an economical use of words. It is therefore quite beautiful when a hymn is able to accomplish more by using just a few lines than is sometimes communicated in an entire sermon. Charles had a knack for doing just that, and two aspects of his Christmas hymns make them especially compelling even today: an emphasis on the freedom from sin that Jesus provides, and the paradoxical contrasts between humanity and the divine that occur in the incarnate Christ.
Salvation as freedom from sin and death:
From one of the hymns that survives in common usage today—"Come, Thou Long-Expected Jesus":
Come, thou long expected Jesus,
born to set thy people free;
from our fears and sins release us,
let us find our rest in thee.
born to set thy people free;
from our fears and sins release us,
let us find our rest in thee.
Riffing on the post-Edenic promise in Genesis 3:15 that the child of Eve would trample the head of the serpent, we have these lines from Nativity Hymn #6 (stanza 5):
Gaze on that helpless object
Of endless adoration!
Those infant-hands
Shall burst our bands,
And work out our salvation
Strangle the crooked serpent,
Destroy his works forever,
And open set
The heavenly gate
To every true believer
Destroy his works forever,
And open set
The heavenly gate
To every true believer
The paradox of the human meeting the divine:
Glory be to God on high,
And peace on earth descend;
God comes down: he bows the sky:
And shows himself our friend!
God th’ invisible appears,
God the blest, the great I AM
Sojourns in this vale of tears,
And Jesus is his name
Emptied of his majesty,
Of his dazzling glories shorn,
Being’s source begins to be,
And God himself is BORN!
And peace on earth descend;
God comes down: he bows the sky:
And shows himself our friend!
God th’ invisible appears,
God the blest, the great I AM
Sojourns in this vale of tears,
And Jesus is his name
Emptied of his majesty,
Of his dazzling glories shorn,
Being’s source begins to be,
And God himself is BORN!
Some modern-day song-writers still attempt to capture these aspects of Charles's songs. Check out, for instance, this track from Cardiphonia that is inspired by the hymn quoted above: "Glory Be to God on High."
Of course, Charlie Brown provides the best popular culture portrayal of one of Wesley's Christmas hymns—"Hark! the Herald Angels Sing." Like the hymns mentioned above, this one grandly proclaims our freedom from sin and death ("born that we no more may die") while playing with the paradox of God-as-man ("veiled in flesh the God-head see").
For more on Charles Wesley and Christmas:
The United Methodist Church has set of devotions based on these hymns, on this site.
If you want a very detailed scholarly treatment, read Frank Baker's article "The Metamorphosis of Charles Wesley's Christmas Hymns, 1739-88."