The shortage of cheer that marked Jimmy Carter's return to overt campaigning in Ohio reflected the problems he faces against Ronald Reagan rather than the outlook for tomorrow's Democratic primary against Sen. Edward Kennedy, where a victory by the president is expected.

Freed from the Rose Garden by finding that the hostage crisis and other problems had become manageable, President Carter paraded through this Democratic stronghold bolstered by: the trappings and power of the presidency; a rhetoric of boosterism that claimed miraculous recovery from the "malaise" of last summer; the political frailty of Kennedy.

But these assets brought no longrange optimism. "Carter will win the primary with votes to spare," a top Carter operative told us. "But he would lose this state to Ronald Reagan and lose it big if the election came any time soon."

Winning Ohio's primary, even if coupled with losses in California and New Jersey, should block threatened last-minute Kennedy machinations to unhorse Carter at Madison Square Garden. But winning in the Garden will have little if any ameliorating effect on laid-off factory workers, unemployed blacks and inflation-pinched households that, until now, automatically have voted Democratic in presidential elections.

Accordingly, Tuesday's eight-state primary windup is no test of Carter's political strength. To the contrary, finally clinching the nomination looks more like a false spring, following Jimmy Carter's winter of discontent.

The political tools used to end that winter and guarantee the Ohio primary show that Carter has no equal in exploiting the less visible powers of his office. A case in point is Cleveland City Council President George Forbes, an influential black who pushed hard last fall for Kennedy to run for president. Partly because of Forbes' influence, county Democratic Chairman Tim Hagan endorsed Kennedy, bringing along the county organization's official backing.

But on Jan. 16 in Cleveland, Carter national campaign chairman Robert Strauss took Forbes and other Ohio Democrats up the mountain to view the terrain of White House blessings waiting to be bestowed. "I've run them without the White House, and believe me it's a lot easier with." He then made clear that support for the president would reap rewards for the supporters.

Stemming a tide of black votes to Kennedy was vital for Carter in northern Ohio. After listening to Strauss, Forbes switched and endorsed Carter. Development grants began to flow to black churches from Washington. The Department of Housing and Urban Development found $44 million for inner-city spending. When one black leader went into his precincts, he deflected congratulations from himself to the president, explaining: "That's not my money; that's Jimmy Carter's money."

This was brought home recently to Kennedy and Rep. Louis Stokes, his top black backer in Cleveland, when they visited influential black Baptist minister Henry Payden. His Holy Trinity Church had just received a $53,000 "tutorial" grant. "You don't take a man's money Monday and then drop him on Tuesday," Payden told Kennedy, politely declining to endorse him.

The extent of these blessings cannot be known, but Carter now seems assured of a respectable black precentage. That may well pin down the Ohio primary. Yet, publicly invisible exploitation of White House power will neither carry over to the November election nor begin to diminish the cheerlessness felt by the mases of rank-and-file voters, especially normally Democratic blue-collar workers.

For them, the president's appeal came over as unabashed boosterism at a $150-a-plate Carter fund-raiser Thursday night, heavily papered with free tickets. ("We were giving away whole tables," one party functionary said.) Carter talked of a United States rapidly curing inflation at home and alliances abroad "that have never been stronger."

Without offering any proof, he saw a "profound difference" in the country's mood since the era of malaise he briefly proclaimed last summer. But Democrats here tend to feel that if there has been any such change, it has been for the worse, not the better; nothing Carter said here changed their minds.

That explains the cheerlessness, and it measures the gap that Carter must cross between now and the Nov. 4 election. Exploiting the patronage power of the presidency and trying to talk away the country's problems are enough against a crippled Kennedy candidacy. Much more will be needed against Reagan.