Eisenhower never voted. I read he was scrupulous about this.
That was the old Regular Army. But even in the Old Army that was more of an ideal than reality. Most of our early generals were political, throughout the 19th century. Both politicians appointed to as generals and generals who went into politics.
In the late 19th and into 20th century, the professional tradition -- including not voting -- developed, but applied primarily below the general officer level. Truly, successful general officers have to be political in one way or another (if not especially partisan). MacArthur was tremendously political (his mother was very well connected, and his father was a Civil War general and later governor of the Philippines), so were Pershing and Patton.
Growing up, I knew lots of professional officers who did not vote, but that hasn't been true since the last of the pre-Vietnam guys (commissions pre-1960) left service.
Generals Winfield Scott and George McClellan both ran for President as serving Army officers. (McClellan resigned his commission on Election Day)