The old year now away is fled,
The new year it is enterèd;
Then let us now our sins downtread,
And joyfully all appear.
Let’s merry be this day,
And let us now both sport and play.
Hang grief, cast care away!
God send you a happy new year.
The name-day now of Christ we keep,
Who for our sins did often weep.
His hands and feet were wounded deep,
And his blessèd side with a spear.
His head they crowned with thorn,
And at him they did laugh and scorn,
Who for our good was born.
God send us a happy New Year.
And now with New Year’s gifts each friend
Unto each other they do send;
God grant we may all our lives amend,
And that the truth may appear.
Now, like the snake, your skin
Cast off, of evil thoughts and sin,
And so the year begin:
God send you a happy new year!
Verse 2 refers to the fact that long before it was New Year's Day, January 1 was the Feast of the Circumcision of Jesus, also known as the Feast of the Holy Name, because it's the eighth day after Christmas. The Anglo-Saxon homilist Ælfric (c.955-c.1010) wrote a homily for January 1, in which he discusses Christian and pagan practices of keeping the New Year. Here are some extracts, in my translation (from this book).
We have often heard that people call this day 'year’s day', as the first day in the course of the year, but we do not find any explanation in Christian books as to why this day should be appointed the beginning of the year. The ancient Romans, in heathen days, began the calendar of the year on this day; the Hebrew people began at the spring equinox, the Greeks at the summer solstice, and the Egyptians began the calendar of their year at harvest. Now our calendar begins on this day, according to the Roman practice, not for any holy reason, but because of ancient custom. Some of our service books begin at the Advent of the Lord. However, that is not the beginning of our year; there is no reason for it being this day, although our calendars continue to put it in this place.
It is most rightly thought that the beginning of the year should be appointed to the day when the Almighty Creator fixed the sun, moon and stars and the beginning of all time; that is the day on which the Hebrew people begin the calculation of their year, as the leader Moses wrote in the book of the law. Certainly God spoke to Moses about the months; this month is the beginning of the months, and it is the first in the months of the year. Now the Hebrew people observe the first day of the year on the spring equinox, because on that day the time of the year was appointed. The eighteenth day of the month which we call March, which you call ‘Hlyda’, was the first day of this world. On that day God created light and morning and evening. Then three days went by without time being measured, because the stars were not created until the fourth day. On the fourth day the Almighty created all the stars and the seasons of the year, and said they were to mark days and years. Now the Hebrew people begin their year on the day when all times were created, that is on the fourth day after the creation of the world. The teacher Bede calculates with great accuracy that the day is the 12th calend of April [i.e. 21 March]. On that day we celebrate that holy man Benedict to honour his great virtues. Indeed, the earth also shows by the shoots which are then quickened again that it is the time when the year should most rightly begin, when it was created.
Now foolish men practise divination by many kinds of sorcery on this day, in great error, according to heathen customs contrary to their Christian faith, so that they may lengthen their lives or their health; but in doing that they anger the Almighty Creator. Many people are also so greatly wrapped in error that they plan their journeys according to the moon and their deeds by the days, and will not let blood on a Monday because it is the beginning of the week - but Monday is not the beginning of the week, it is the second; Sunday is foremost in order of creation, in order, and in honour.
Some foolish people also say that there are some kinds of cattle which man should not bless, and say that if they are blessed they go wrong, but are made obedient by cursing, and use God’s grace to injure them with the devil’s curses, without blessing. Every blessing comes from God, and curses from the devil. God made all creation, and the devil cannot create anything; he incites to evil and acts falsely, the origin of sin and deceiver of souls. Any part of creation which seems perverse has been brought low by sin. Holy men often lived in the desert among fierce wolves and lions, among all kinds of animal and serpent, and nothing was able to harm them; they tore horned snakes apart with their bare hands and easily killed great dragons without any harm through the power of God.
Now you observe the days and months with vain sorcery. However, according to nature every bodily creation which earth brings forth is more full and vigorous at the full moon than at the waning; trees which are cut down at the full moon are harder and last longer as timber, most of all if they are sapless. This is no sorcery, but a natural thing, created. So, also, the sea agrees wonderfully with the course of the moon; they are always fellows in waxing and waning, and when the moon daily rises four prican (= fifth of an hour) later, so also the sea always flows four prican later.
Let us set our hope and happiness in the foreknowledge of the Almighty Creator, who established all creation in three things: that is in measure, number and weight. To him be glory and praise for ever world without end. Amen.