Each of the Celtic Mythologies (Britain, Wales, Ireland & Scotland) contains a version of the Battle of the Oak King and the Holly King. These two kings each rule half of the year and they fight for supremacy as the seasons change each year.
Each year, the Oak King challenges and is victorious over the Holly King. Ruling until the Holly King returns and challenges him again. And so the cycle repeats and the world turns.
Some cultures have the kings battling at the equinoxes, when the day and night are of equal length. This means that mid winter and mid summer are when the Kings are at the peak of their power. Some have them battling at the Solstices and peaking in power at the Equinoxes. Which ever timing makes the most sense to you, the important theme of this legend is the balance of the seasons and the changing energy of the continually turning wheel of the year.
No matter which way you interpret this myth, or what time of year you acknowledge it. It is firmly based in balance. The balance between night and day, light and dark, resting and growing.
To me it makes sense to honor the battle at the Equinoxes, and then at mid summer and mid winter, acknowledge the King at the height of his glory and power. The Holly King supreme on the day when night is longest, before he begins his fight against the encroaching light, wrapping the cold deeper and tighter around the earth to prove he is supreme. Only to finally begin to give way at Imbolc and lay down his weapons at Ostara when the Oak King returns, bringing with him light and growth and fertility. Repeating the cycle by growing in strength and brightness until Mid Summer when the growing darkness heralds the return of the Holly King and causes the Oak King to blanket us in hotter days to remind us of his power.
Which days you honor each energy is far less important than understanding that this myth and this cycle speak to us of the balance of light and dark, activity and rest. That we take this to heart and do what we can to balance our own lives, adjusting our activities in a way that for us honors this change.