Snyder defeated four other candidates seeking the two-year term.
Rodney Pierce won the treasurer's post, defeating incumbent president Robert Odawi Porter for that position.
Snyder said in a news release, "Nya-Weh. I want to thank the Seneca people for once again believing that leadership of our Nation is by the people. The past two years have broken the spirit and confidence that our people have in Seneca political leadership. We will not look back but we will move forward with an open and transparent government that will enable us to continue to protect and grow our economic sovereignty and our traditional values and culture."
Snyder received 929 votes. 2,636 votes were cast at polling places on both the Cattaraugus and Allegany territories.