President Carter announced yesterday he will appoint Frederick H. Schultz, a multi-millionnaire banker-politician from Florida who was a key financial backer of presidential pollster Patrick H. Caddell, to the Federal Reserve Board.

Carter also nominated Emmett J. Rice, senior vice president of the National Bank of Washington to a second vacancy on the board. Rice, if confirmed, would be only the second black to serve on the board.

The two new nominations would bring the number of Carter appointees on the board to four out of the seven-member total. Carter also appointed Fed Chairman G. William Miller and Fed Chairman G. William Miller and Fed member Nancy Teeters. He reportedly chose Rice to ensure a black on the board.

The nominations could prove pivotal. Carter's top economic advisers, fearful the economy is overheating, are considering asking the Fed for selective credit controls. Since the agency is independent, Carter would need majority support. Carter is also seeking a rise in interest rates.

There appeared to be little question that Rice's nomination would be confirmed by the Senate. The 50-year-old South Carolina native served as alternative U.S. executive director to the World Bank in the late 1960s, and earlier worked in the Treasury Department.

However, there were indications that Schultz' appointment might come under close scrutiny in Congress, in part because of his Florida political activities.

Sen. William Proxmire (D-Wis.), chairman of the Senate Banking Committee, said yesterday "Rice sounds qualified, but this other guy-I don't know." Proximire said his panel "will want to take a good long look" at Schultz' record and qualifications.

Schultz, 50, is chairman of the board of Barnett Investment Services, Inc., a subsidiary of Barnett Banks of Florida, one of the largest bank holding companies in the state. Barnett Banks, with $3 billion in assets, operates more than 40 banks with about 80 offices throughout Florida. Schultz is also a director of the holding company.

After attending Princeton University and the University of Florida Law School, Schultz was employed in the executive training program of the Barnett National Bank of Jacksonville from 1956 to 1957. He then opened his own office, the White House announcement said, "concentrating his efforts in securities markets and in providing risk capital for new and expanding ventures."

The Federal Reserve regulates many bank holding company activities, as well as those of national banks such as Barnett, which must be members of the Fed system.

Schultz was described by one Florida political source as "a man with no enemies." He was a member of the Florida state House from 1963 to 1971, and served as speaker his last two years in office.

In 1970 Sen. Lawton Chiles (D-Fla.) nosed out Schultz for the runner-up position in a five-way primary fight for the Democratic nomination for the U.S. Senate. Chiles went on to win the runoff, and later the election.

Schultz has not run again her elected office, having relinquished his House seat to try for the U.S. Senate. He was regarded as a "progressive" in Florida politics. Last year Carter appointed him to an advisory commission on education.

Schultz' financing of Caddell's polling enterprise is an example of the type of loans "venture capital" providers usually make - high-risk but with a very large potential payoff.

Rice and Schultz are both Democrats. They would replace a Democrat, Philip Jackson, who resigned, and Stephen Gardner, a Republican banker, who died.

Rice, and economist, received his Ph.D. from the University of California in 1955 and taught at Berkeley and Cornell before joining the Federal Reserve Bank of New York in 1960. From 1960 to 1964, Rice assisted in establishing the Central Bank of Nigeria after that country gained its independence.* CAPTION: Picture, EMMETT RICE . . . D.C. banker