Horsey was born in Little Creek Hundred, near Laurel, Delaware. First living in Georgetown, Delaware, he moved to Wilmington, and studied the law there under James A. Bayard, who remained his lifelong political mentor. A frequent supporter of education, Horsey, early in his career, urged the establishment of a library in Georgetown, and later was appointed a trustee of the College of Wilmington. He was admitted to the Delaware Bar in December 1807, and began a practice in Wilmington. He married Elizabeth Digges Lee, daughter of Thomas Sim Lee of Maryland.
Professional and political career
While practicing the law and after representing Sussex County in the State House from the 1801 session through the 1803 session, Horsey was appointed to be the Delaware Attorney General and served from 1806 to 1810. In 1810 he was elected to the U.S. Senate to fill the vacancy caused by the death of U.S. Senator Samuel White. In the Senate he initially opposed the War of 1812 strongly, but once it had been declared, he supported it with equal vigor. He accordingly became a member of the Committee of Safety and was actively involved in preparing the defenses of Fort Union and Wilmington. In March 1814 Horsey presented a petition from the citizens of Delaware to repeal the Embargo Act of 1807; although he was able to get a committee appointed to consider the question, the effort was ultimately unsuccessful. He was reelected in 1814, and served from January 12, 1810, to March 3, 1821. Following the War of 1812, but while still a contentious subject, the need for internal improvements had become much more apparent and recognized. It would be on Horsey's motion in January 1816, that the Senate finally passed the resolution to print and distribute copies of Treasury Secretary Albert Gallatin's 1808 Report on the Subject of Public Roads and Canals. The report, which had been requested by the Senate in 1807 and transmitted to it in 1808 had fallen victim to the embargo, the loss of revenue, and the necessities of war. With the report's distribution, many of its concepts would be incorporated into the Bonus Bill of 1817. Several years later, he parted ways with the Delaware General Assembly which had passed a resolution asking Delaware's congressmen to vote against any extension of slavery. Horsey did not feel U.S. Congress had the right to prohibit slavery in Missouri, or anywhere else in the Louisiana Purchase, and so supported the Missouri Compromise. Understanding the unpopularity of this position he did not seek reelection when his term ended. During the 16th Congress, he served as Chairman of the Committee on the District of Columbia.
Elections were held the first Tuesday of October. Members of the State House took office on the first Tuesday of January for a term of one year. The General Assembly chose the U.S. Senators, who took office March 4 for a six-year term. In this case he was initially completing the existing term, the vacancy caused by the death of Samuel White.