Most records dealing with Wood's personal life have been lost due to fire or other causes. As a result many details about his life are unknown. Wood was born near Cuthbert, Georgia on March 12, 1795. His mother was Elizabeth Burris Wood. His father, name unknown, died when he was five. When he was nineteen, Wood raised a company of volunteers for the Creek War and fought in the Battle of Horseshoe Bend. According to tradition, Wood met Sam Houston and Edward Burleson during the campaign. Wood operated a successful dry goods business based in Cuthbert. During a buying trip in 1837 he met a young widow named Martha Evans Gindrat, daughter of Jesse and Elizabeth Evans, during a stop in Milledgeville, Georgia. The two married on September 18, 1837. The marriage produced two children in addition to the three Martha brought from her previous marriage. Beyond his business interests, Wood was a member of the Georgia General Assembly from 1837–38.
The 1847 decision of Governor James Pinckney Henderson to not seek another term left a wide open race for his replacement. A race dominated by five candidates developed with the key issue being how to deal with the public debt. About a month before the election one of the candidates, Isaac Van Zandt, died of yellow fever. Most of Van Zandt's support shifted to Wood. As a result he won the election with 7,154 votes compared to second place finisher James B. Miller with 5,106. When the governor took office, Texas had US$5,500,00 in outstanding bonds with no obvious means to repay the debt. To deal with the public debt, he advocated a plan to sell state land to the U.S. Federal government. The Texas Legislature did not support this plan and, after negotiations with Wood, passed a bill calling for the state Accountant and comptroller to determine the exact amount of debt before a method of payment was determined. The Wood administration also saw an intensification of a dispute over the status of New Mexico. Texas considered New Mexico part of its territory but the claim was not recognized by the Federal government. To strengthen its claim, the Texas Legislature created Santa Fe County and the eleventh judicial district. When the judge appointed to preside over the new district arrived in Santa Fe, he found federal troops already in the city who were determined to support the federal position. Other issues dealt with by Wood were the organization of towns and counties, establishing court buildings, and reforming government operations. To defend the state's western frontier, a request was sent to Congress asking for a string of forts to be constructed. Reapportionment of the state was the most contested issue to arise during Wood's term. The coastal and central sections of the state, fearing loss of representation, opposed the proposal while the northeastern section supported the effort. Despite the opposition, a reapportionment bill was passed by the legislature. On February 21, 1848, Wood presided over the Texas Democratic convention, the first true political convention to be held in the state. This was followed by an 1849 effort to win a second term. The primary challenger to the governor was Peter H. Bell who ran on the issues of frontier defense and the New Mexico dispute. Wood strongly defended the positions he had taken but was defeated by a margin of 10,319 votes to 8,754.
Later life
After leaving office, Wood returned to his farm. In addition to his plantation, he established a mercantile business in Galveston. He made unsuccessful runs to be elected Governor in 1853 and 1855. He died at his home on September 3, 1858.