Behind that army of hungry children being mobilized against President Carter's proposed cuts in school feeding programs, some of the country's biggest food companies are rolling up the heavy artillery.

Pizza makers, cereal makers, fruit growers, french-fry producers, turkey vendors and cookie bakers, among others, want to save the golden goose from Carter's budgetary axe.

Heavily dependent on school lunch sales, they have organized something called Project SMILE (School Meals Industry for Learning in Education). c

SMILE's better-known members include the Kellogg Co., Sunkist Growers, Chiquita Brands, the Cling Peach Advisory Board, Archer-Daniels-Midland and the Keebler Co., as well as distributors and food equipment firms who find financial calories in school lunchrooms.

Their group provides another of those occasional illustrations of the complexity of this town. Things are not as simple as they sometimes seem. A school breakfast not served is also, eventually, a kernel of corn not flaked.

Cutbacks in federal school feeding most likely will be felt sooner by food suppliers than by the children although the children's surrogates have done the loudest public complaining, until now. This week a delegation from Project SMILE, headed by founder and pizza maker Louis Sabatasso of Santa Ana, Calif., has been in town.

The Carter administration's January budget proposed a reduction of about $400 million in fiscal 1981 support for feeding programs, a proposal that set off alarms among school lunch administrators.

When the Senate Agriculture Committee last week went along with similar cuts in its recommendations to the Senate Budget Committee, the Project SMILE people began taking the fiscal-restraint cries seriously.

Hence the delegation to Washington. They saw Sen. George McGovern (D-S.D) Tuesday and contacted the staff of Sen. S. I. Hayakawa (R-Calif.) yesterday to plead for the welfare of children's tummies.

The administration's proposed cuts would reduce direct feeding payments by five cents a meal, which translates to about 30 percent of the subsidy -- a sharp blow to lunch programs. Other rules changes also would reduce program costs.

"A lot of kids won't get to eat if these cuts are approved," a publicist for SMILE said yesterday. "Everyone has been bad-rapping the schools and their meal programs. We wanted to get it to the public that these industries are trying to put something back into the programs."