From the Diocesan Office for Divine Worship,
Covering Crucifixes and Statues
The tradition of covering statues and crosses likely has its roots in the medieval usage of a veil to cover the entire sanctuary during the Lenten season. There is evidence of this since the 9th century in Germany where a “Hungertuch” (hunger cloth)) was in place throughout Lent until Wednesday of Holy Week when, during the proclamation of the Passion, it was taken down at the words “the veil of the temple was torn in two.”
What has been handed on to us today is a vestige of this practice noted in the Roman Missal for the 5th Sunday of Lent. This Sunday traditionally brings the Church into the time of “Passiontide” wherein the intensity of our preparation for the Lord’s Passion, Death and Resurrection is increased. To cover the statues deprives the visual senses of the joy of seeing the fruit of the Paschal Mystery exemplified in the saints. It likewise forces the mind and the heart to focus more intently on the central acts of Christ’s redeeming work of love.
Stained glass windows and Stations of the Cross remain uncovered during this time. And, the processional cross is not veiled since its usage is implied in the rubrics for Palm Sunday and Holy Thursday.
The covering of crosses remains in place until the end of the Celebration of the Lord’s Passion on Good Friday while the statues are to be covered until a convenient time before the start of the Easter Vigil.