Hymns are all about symbols. No one believes that Bethelehem was covered in snow, or that a Christingle orange really represents the world, it's only a way of representing a Christmas tradition, or what would become a Christmas tradition.
A carol is different from a hymn. According to its use in mediaeval English it was a folk song, even if now it is used at Christmas. So "We Wish You A Merry Christmas" is a carol as it The Wassail Song but neither is a hymn. A hymn is simply the Greek word for "a song of praise", usually dedicated to a god. The word was adopted by the Christian religion.
It seems that many fans of classical music find most of the popular hymns old hat. Their top five are: 5: Lulla, Lullaby (The Coventry Carol). 4: Bethlehem Down. 3: A Spotless Rose. 2) In Dulcio Jublio ("In Sweet Rejoicing"). 1) In The Bleak Midwinter. There were other well known songs in the top 25; Silent Night at 25, We Three Kings at 23, God Rest We Merry Gentlemen at 22, Hark the Herald Angel Sing at 14, Once in Royal David's City at 11 and O Come All Ye Faithful at 8. Maybe it's better to concentrate on the hymns people know though?
Still it might be worth dwelling on In The Bleak Midwinter a bit longer. Its word came from a poem by Christian Rossetti, the sister of Pre-Raphaelite artist Dante Gabriel Rosetti. Unlike many carols it goes into a host of different angels, not just angels and archangels but also cherubim and seraphim. Seraphim are angels with six wings while cherubims (not to be confused with cherubs) are the angels said to guard the Garden of Eden.
Although many hymns are obviously about Christ, some are a bit more obscure. Good King Wenceslas may be about celebrating a Czechoslovakian King, but it is also a stand in for Christ as well as being about the spirit of Christmas.
The main themes of most hymns tend to be the nativity, though some chose to focus on the Shepherds and some focus on the Wise Men. There are hymns which focus on a new character, such as The Little Drummer Boy and Barbushka. The moral of the first is that we give our music as a gift to Christ and the moral of Barbushka is that you can't delay things if you wish to see Christ.
Ding Dong Merrily On High would seem to suggest that on Christ's birth, all the bells were ringing. Religion and bells seems to go back to Exodus, where "tinkling was heard when Aaron entered and leaves holy places before the Lord". Huge church bells and tower bells would be a mystery to most people in the Holy Land at the time of Jesus though.
How do you explain "Priests and people swung them"? There were Magi but no priests knew about Christ's birth. Not that you should take these things too literary.
We Three Kings names the Magi as Caspar, Melchior and Balthazar. These names come from a Greek document of about 500 AD but seems not to have much authenticity behind it. The hymn itself seems a celebration over the Feast of Ephinany rather than Christmas itself, which is 12 days after the main event.
We might link ourselves more with the shepherds. While Shepherds Watched Their Flocks goes all the way back to 1696. The alternative name Sweet Chiming Bells are due to an additional chorus. There is another chorus which starts "Hail, Chime On, Chime On".
Whatever hymn is your favourite it seems that these songs make Christmas so enjoyable, whether it's a Midnight Mass service or the big day itself.