Was the full Sign of the Cross prevalent in entire Catholic Church?

As a member of the Syrian Rite Catholic Church, I was taught to make a full Sign of the Cross while entering the church, while starting a long prayer etc. While the sign made is similar to the one made by the faithful at the commencement of the Gospel-reading in the Holy Mass (Latin rite), the prayer that accompanies the sign is different. It can be roughly translated as: " By the sign of the Holy Cross, save us from from our enemies, our Lord, in the name of the Father, the son and the Holy Spirit, Amen. " I wish to know if the said custom of making the Sign of Cross during which one makes cross-signs on one's forehead, lips, chest and shoulders, while reciting the prayer, was prevalent in the entire Catholic Church , and whether it was later substistuted with the smaller Sign of the Cross .