Answer:
Most stayed where they were and became US Citizens.
Actually, they were not allowed citizenship immediately. Some "emigrated" into Mexico while others remained in the new US territories. However, those who did remain were relegated into a lower social sphere like the Native Americans, Blacks and Mormons of the early 19th Century. Many US Congressmen and Senators of the period did not support the war simply because they did not want to create a nation that would not be prodominantly white, like Sen. John C. Calhoun of South Carolina. Calhoun once argued against a full conquest of Mexico saying, "Ours is the government of the white man." (Howe, What Hath God Wrought, pp. 798-99)