1. On January 3, 1776, General John Sullivan led an American army against British forces at the Battle of Quebec, Canada. Although the battle ultimately ended in defeat for the Americans, it marked an important turning point in the Revolutionary War.

2. In 1809, the town of Nashua, New Hampshire was incorporated on January 3. Nashua quickly became an important industrial center, known for its textile mills, and eventually developed into a prosperous city.

3. On January 3, 1861, New Hampshire Governor Ichabod Goodwin delivered his inaugural address, in which he strongly supported the Union and opposed secession by southern states. New Hampshire was one of the first states to send troops to fight for the Union during the Civil War.

4. In 1929, Wilkins H. Dow became the governor of New Hampshire on January 3. Dow was the first Republican governor to serve two consecutive terms in the state, and he was known for his efforts to modernize the state's infrastructure.

5. On January 3, 1972, the New Hampshire Supreme Court issued its landmark ruling in the case of State v. Piper, which declared that the state constitution protected a woman's right to choose to have an abortion. This decision made New Hampshire one of the first states to recognize such a right.