Snow was the fifth child and first son of Oliver Snow and Rosetta Pettibone, residents of Mantua, Ohio, who had left New England to settle on a new and fertile farm in the Connecticut Western Reserve. Despite the labor required on the farm, the Snow family valued learning and saw that each child had educational opportunities. Lorenzo received his final year of education at Oberlin College, which was originally founded by two Presbyterian ministers. Snow later made his living as a school teacher when not engaged in church service.
On his recovery, Snow left for a second mission to Illinois and Kentucky in the fall of 1838. He served there through February 1839, when he learned that the Latter Day Saints had been expelled from their settlements in Missouri. He traveled home by way of his former mission area in Ohio. He was again taken ill and was cared for by members of the church. He remained in Ohio, preaching and working with church members until the fall of 1839. During the school year of 1839–40, Snow taught in Shalerville, Ohio. He sent money to his family, which had by then settled in Nauvoo, Illinois. He joined them in May 1840.
Shortly after he arrived in Nauvoo, Snow was again called to serve an active mission, this time to England. After an unpleasant sea voyage from New York City, Snow met with some of the members of the Twelve Apostles who had opened the British Mission in 1839, including Brigham Young, Heber C. Kimball, and Parley P. Pratt. He worked briefly in the Manchester area, and had success in Birmingham, where he baptized people in Greet's Green and organized a branch in Wolverhampton. Snow was then assigned to preside over church members in London. During his administration, church membership in the city increased from 100 to approximately 400 members. He was released from his mission by Pratt, who by then was president of an expanding European Mission. Snow arrived home on April 12, 1843, bringing with him a shipload of 250 British converts.
After visiting with his family, Snow again secured a teaching position for the winter, teaching at Lima, Illinois, thirty miles from Nauvoo. In late spring 1844, he returned to Ohio, preaching and baptizing new converts and distributing recent church publications to members. He was working in Cincinnati, Ohio when he learned of the assassination of Joseph Smith. Snow closed his Ohio mission and promptly returned to Nauvoo.
During the period of disorganization and schism that followed Smith's death, Snow chose to follow the Quorum of the Twelve under Brigham Young. In 1845, Snow was involved in work in the Nauvoo Temple.
Shortly after his call to the Twelve, Snow left on a mission to Italy and French-speaking Switzerland. He later sent missionaries under his direction to India (1849–1852). Snow was directly involved in missionary work in Italy and Switzerland, and also visited Malta. He had planned to visit India, but various circumstances prevented this journey.
In 1851, Snow published a pamphlet entitled "The Italian Mission about his and his companions efforts in Italy. It was published in London.
Snow wrote a pamphlet entitled "The Voice of Joseph" in 1850 to advance missionary work in the Italian mission. He was unable to find anyone in Italy to translate it so sent it to Orson Pratt, then the president of the British Mission, who eventually found someone in Paris to translate it.
The efforts of missionaries under Snow, especially the ones he sent to Turin, inspired an article attacking the Mormon missionaries for undermining the Roman Catholic Church in the Turinese paper, L'Armonia. Snow and his successors were unsuccessful in the cities also due to opposition to their activities by the government of Camillo Cavour.
In 1853, under the direction of church president Brigham Young, Snow founded Brigham City, Utah. Settlement had began on a limited scale at this site under the name "Box Elder". Snow changed the name and moved the community towards living up to its name. He was also a key backer of the Brigham City Cooperative, which was the inspiration for ZCMI and other cooperatives.
In 1864, Snow was sent on a mission to the Sandwich Islands. He went on this mission with Ezra T. Benson and Joseph F. Smith. They were responding to messages from Jonatana Napela and other Hawaiian church members about the irregular administration of the church by Walter Gibson. While here, Snow was seriously injured but was healed through the ministration of holders of the priesthood.
In 1888, Snow went to Rexburg, Idaho. While here he told the leaders of the stake that Karl G. Maeser had been appointed Commissioner of Church Education and recommended that they form a stake academy. The local leaders followed Snow's instructions and the institution they formed eventually evolved into Brigham Young University–Idaho.
As he began his tenure as president, Snow had to deal with the aftermath of legal battles with the United States over the practice of plural marriage. Men engaging in plural marriage were still being arrested and confined in Utah Territory. Some members of the LDS Church did not accept the 1890 Manifesto put forth by Wilford Woodruff, and there was a strong division of opinion on plural marriage even in the priesthood hierarchy of the church.
The LDS Church was also in severe financial difficulties, some of which were related to the legal problems over plural marriage. Snow approached this problem first by issuing short term bonds with a total value of one million dollars. This was followed by emphatic teaching on tithing. It was during this time that the LDS Church officially adopted the principle of tithing, the payment of 10% of one's income, as a hallmark of membership. Snow gave an address at the St. George Tabernacle in St. George, Utah, imploring the Latter-day Saints to pay tithes of corn, money or whatever they had in order to have sufficient rain. After much patience and faith, it rained in southern Utah. In a short period of time, the members' practice of paying a tithe reduced the church's debt and financial difficulties to a manageable level.