Winbeck originally enlisted in the Coast Guard in 1923 and was stationed at Coast Guard Station Cape Disappointment. In 1926, he entered the United States Coast Guard Academy. He graduated and received his commission in 1929.
During World War II, Winbeck first served aboard the USS Arthur Middleton (APA-25). After being assigned to Coast Guard District 13, he became Executive Officer of the USS General H. L. Scott (AP-136), serving in the Pacific Theater of Operations. The following year, he assumed command of the ship.
Winbeck became Chief of Personnel of the Coast Guard in 1957, an assignment which also placed him in charge of the United States Coast Guard Reserve. The following year, he was named Commanding Officer of District 13.
Winbeck retired in 1964, at which time he was awarded the Coast Guard Commendation Medal. He died in 1990.