Saint Stephen's Day is the first day after the celebration of Christ's birth, in honor of Saint Stephen having been the first of Jesus' followers to become martyred. Stephen was stoned to death.
On Stephen's Day, on old and no longer practiced tradition involved the letting of horses blood. The thinking was that this would protect the horses against sickness in the coming year.
More from Marmion:
"...Then followeth Saint Stephen’s Day, whereon doth every roan
His horses jaunt and course abroad, as swiftly as he can.
Until they do extremely sweat, and then they let them blood,
For this being (lone upon this day, they say doth do them good,
And keeps them from all maladies and sickness through the year,
As if that Stephen any time took charge of horses here...."