Moses H. Cook was born on August 25, 1801, in Lenox, New York, to Moses Harper Cook and Polly Pyson. He moved to Ohio in 1834 and married Hannah C. Pixley. They had at least four children: Joseph, born around 1836; Myron, born around 1843; Alice, born around 1846; and Francelia, born around 1853. They lived in Ohio until the early 1840s, when they moved to Crete, Illinois.
Cook worked as a farmer there, and by 1850, he owned $1,200 of real estate. He was elected town moderator in 1850. A decade later, he owned $4,000 of real estate and $1,000 of personal property, and by 1870, he had $700 of real estate and $540 of personal property. He supported the United States Christian Commission, donating $1 in January 1865. He retired sometime in the 1870s, and he died on November 17, 1882.