In 1990, Cozzens was arrested several times for blocking access to facilities that provided abortion services for women, at one point spending ten days in jail.

Cozzens earned his Doctorate of Sacred Theology from St. Thomas in 2006 with a dissertation entitled Imago Vivens Iesu Christi Sponsi Ecclesiæ: The Priest as a Living Image of Jesus Christ, Bridegroom of the Church, through the Evangelical Counsels.

[8] After returning from Rome, Cozzens was appointed as an assistant professor of sacramental theology and director of liturgy at the Saint Paul Seminary.

"[10]At the June 2021 meeting of the United States Conference of Catholic Bishops, Cozzens, as chair of the Evangelization Committee, announced a nationwide Eucharistic Revival to begin in 2022.

[citation needed] In July 2024, Cozzens joined other Catholic bishops in condemning a controversial scene in the opening ceremonies of the 2024 Paris Olympics.

The performance appeared to recreate Leonardo da Vinci's Last Supper painting, with drag queens portraying the apostles and a DJ as Jesus.