It is said that seeing a robin during winter was a sign that the Oak King and summer would return. The robin is associated with the Oak King and the wren associated with the Holly King. Both the robin and the wren can be seen during the winter and summer months, it's a sign of the Oak Kings reign however it is also a reminder that the Holly King is never far away.
In Celtic myth and legend the Oak King is comparable to the Green Man, a legendary being who is a symbol of rebirth. The Green Man like the Oak King was seen as a figure of fertility and is most commonly depicted as having a face made from sprouting oak leaves whereas the Holly King is depicted as having a face made from sprouting holly leaves. Both are a symbol of seasonal renewal.
It is believed that the Oak King and the Holly King are brothers and represent their reign and defeat over one another, twice a year, through transformation at the equinoxes, Spring and Autumn, with the Holly King ruling over the dark part of the year and the Oak King ruling over the light part of the year.