President Reagan's State of the Union vow to push on with his economic program and his refusal to seek new tax increases this year to reduce future budget deficits hit Wall Street with the thud of a falling snowflake today.

But late in the day and well after the close of major stock markets, the U.S. Treasury surprised Wall Street with a $2.5 billion long-term bond offering and bond prices fell sharply.

Stock prices traded in a narrow range from open to close and happened to close slightly higher. The Dow Jones 30-stock industrial average, which was down 2.47 points at 3 p.m., finished up 1.15 to close one hour later at 842.66.

Bond prices, which climbed about $7.50 per $1,000 of face value in the early hours of trading, receded to their opening levels by 4 p.m. But in the usually light trading that goes on after 4 p.m., prices fell $7.50 on word that the Treasury's long-term portion of a $10 billion refunding package was much larger than expected. Some traders stopped making quotes within minutes of the announcement.

"I guess bond traders liked the way he delivered the State of the Union address," said Bernard Harmon of the brokerage firm Drexel Burnham Lambert Inc.

But on balance, Reagan's Tuesday night address seemed to have little impact on the course of business in today's financial markets, except perhaps to boost trading volume in stocks.

Many institutional investors, such as pension funds and insur ance companies, held off buying or selling stocks Monday and Tuesday to wait to see what the president would say. They bought and sold heavily today, but in no distinguishable pattern of panic or euphoria, according to Jerry Hinkle, chief trader for Sanford C. Bernstein & Co., a brokerage firm that deals mainly with institutional clients.

As a result, volume on the New York Stock Exchange was up today. More than 50 million shares of stock changed hands there today, compared with 44 million on Tuesday. Nationwide turnover of NYSE-listed stocks on all exchanges was 57.67 million shares. The number of NYSE issues that closed higher for the day outnumbered those closing lower by 776 to 636.

The New York Stock Exchange's own index was up 0.29 point to 66.78. The American Stock Exchange index was up 0.63 point to 279.67 and the National Association of Securities Dealers index for the over-the-counter market rose .16 point to 183.57.

That stock prices did not decline today should be taken as a vote of confidence for Reagan, Hinkle said. Under normal circumstances his refusal to seek tax increases--or "revenue enhancements" as they are called in the euphemistic jargon of the Reagan administration--would have triggered a sell-off. "Investors are saying, 'Hey, the president's right. If his program is going to work, it will take time,' " Hinkle said.

But in recent years investors have not been noted for their long-time horizons. The weekly money supply report, a figure that economists say has little meaning, can send bond prices rising or falling $10 in seconds. The president's resolve to carry on with his tax cuts virtually assures sizeable budget deficits in the coming years that will keep federal borrowing and interest rates high and might force the Federal Reserve, the nation's central bank, into running a tighter monetary policy than it otherwise would.

In the bond markets, where interest rates remain high and investors remain reluctant to commit themselves to 30-year investments, trading was light, Drexel Burnham's Harmon said. Unlike the stock market, where institutional purchasers dominated, individual purchasers were the main force.

Two Washington-area firms were among the top three OTC stocks today, in volume. MCI Communications, a competitor for long-distance telephone service, rose $1.50 a share to $31 on a volume of 337,600--largest of the day. Maryland National Corp., owner of Maryland National Bank, ranked third in volume with 253,400 shares and rose 25 cents to $20.75.