Many of the earliest Sabbatarian Adventists rejected a belief in the Trinity for a variety of reasons. With time, these anti-Trinitarian views were modified, largely because Ellen G. White's views continued to develop.
In 1850 Ellen G. White confirmed the personhood of Jesus Christ and God the Father, stating, "I have often seen the lovely Jesus, that He is a person. I asked Him if His Father was a person and had a form like Himself. Said Jesus, 'I am in the express image of My Father's person." (Emphasis is in original. Early Writings 77; c.f. 51, 54).
In subsequent years, Ellen White made further advancements in her understanding of the Godhead. In 1897-1898 Ellen G. White made her first statement regarding the personhood of the Holy Spirit, stating that He was "the third person of the Godhead" (Special Testimonies, Series A10 25, 37). Similarly, she wrote that the Holy Spirit was "the Third Person of the Godhead" in 1898 in Desire of Ages (p. 530, 671). Other statements include, "the Holy Spirit . . . is as much a person as God is a person" (Evangelism 616); and, "The Holy Spirit has a personality, else He could not bear witness to our spirits and with our spirits that we are the children of God. He must also be a divine person, else He could not search out the secrets which lie hidden in the mind of God." (Evangelism 617).
Therefore, by the late 1890s (if not earlier), it is evident that Ellen G. White believed that God is one and that He is comprised of three co-equal persons: Father, Son, and Holy Spirit. In expressing this view, she never used the word, "Trinity," but preferred the phrases, "three highest powers in heaven," or the "heavenly trio."
Please consult the following sources for a more detailed answer:
Karen K. Abrahamson and John T. Baldwin, "Holy Spirit," in The Ellen G. White Encyclopedia, Denis Fortin and Jerry Moon, eds. (Hagerstown, MD: Review and Herald, 2013), 874-876.
Jerry Moon, "Godhead," in The Ellen G. White Encyclopedia, Denis Fortin and Jerry Moon, eds. (Hagerstown, MD: Review and Herald, 2013), 843-844.
Jerry Moon, "The Adventist Trinity Debate, Part 1: Historical Overview," Andrews University Seminary Studies 41 (Spring 2003): 113-129.
Jerry Moon, "The Adventist Trinity Debate, Part 2: The Role of Ellen G. White," Andrews University Seminary Studies 41 (Autumn 2003): 275-292.
Tim Poirier, "Ellen White's Trinitarian Statement: What Did She Actually Write?" Ellen White and Current Issues Symposium 2 (2006): 18-40.
Woodrow W. Whidden, Jerry Moon, and John W. Reeve, The Trinity: Understanding God's Love, His Plan of Salvation, and Christian Relationships (Hagerstown, MD: Review and Herald, 2002).