A few comments, speaking from a Byzantine Catholic perspective:
The Rosary is a Latin devotion. That is not to say it is not a fine prayer, but to deny that it was born in the Latin Church or that its prayer forms are Latin is as foolish as saying the Mass isn’t Latin but is Universal. The Byzantine tradition does not make use of the Apostles Creed but uses the Nicene Creed exclusively and the Our Father and the Hail Mary (Angelic Salutation) have different forms:
Our Father, who art in heaven, hallowed be
thy name, thy kingdom come, thy will be done, on earth
as it is in heaven. Give us this day our daily bread,
and forgive us our trespasses as we forgive those who
trespass against us, and lead us not into temptation
but deliver us from evil. For yours is the kingdom and the power and the glory, Father + Son, and to the Son, and to the Holy Spirit, now and ever, and forever. Amen.
Hail, Mother of God, Virgin Mary, full of grace, the Lord is with you. Blessed are you among women, and blessed is the fruit of your womb; for you gave birth to Christ, the Savior and Redeemer of our souls.
Is it a Latinization if an Eastern Catholics use it? It depends. If it replaces the Divine Office, the Akathist, or Canons of the Theotokos yes, especailly since private devotion cannot be compared with the official Liturgical Prayer of the Church. If it is intergrated into ones prayer life without displacing anything else, then no. Unfortunately, those who are attached to it often seek to have it recited publically before Liturgy which is wrong because this is properly the time for Matins and/or the First and Third Hours or an Akathist or a Canon as all these are traditionally part of the rule of preparation for receiving Holy Communion and are officially prescribed by the Liturgical Books of the Byzantine tradition.
St. Seraphim didn’t pray the Rosary. He prayed 150 Byzantine Angelic Salutations on a chotki or lestovka, comparible to but not the same as the Dominican Rosary.
Fr. Deacon Lance