Prior to the post-Vatican 2 reforms, the gospel for the 5th Sunday in Lent ended with Our Lord hiding Himself from those who wished to stone Him. Thus, he was hidden for a short while, and from this grew the custom of veiling all crosses, statues, and images. This Sunday became known as Passion Sunday, a term that is now largely associated with Palm Sunday. However, churches that use the Extraordinary Form still keep Passion Sunday and the mini-season of Passiontide during the last two weeks of Lent. During this time, as you point out, images are veiled.
Some parishes veil for just Holy Week, and others not at all. However, even in the current missal, the rubrics give permission to veil beginning on the 5th Sunday in Lent.