It was not quite a rerun of the Civil War, but the House Appropriations Committee, admitting it was outflanked by the South, scored one yesterday for the North.

The committee decided to revamp the formulas for handing out $1.8 billion in energy assistance to low-income families in fiscal 1981, giving more aid to northern states.

"Russell Long pulled a fast one on us," said Rep. Silvio O. Conte (R-Conn.), "and we didn't see what was happening. He took care of Louisiana and other southern states. We're changing that."

Sen. Russell B. Long (D-La.), chairman of the Senate Finance Committee, authored the formulas that assured Louisiana and neighboring Sunbelt states would benefit handsomely in energy assistance from the windfall profits tax on oil.

The new formula, if it survives a final House vote next week and then gets past the Senate, would provide greater energy aid to low-income people in the colder Northern states instead.

Energy assistance is one part of the $84.5 billion appropriation the committee approved yesterday for labor, health and human services programs in the next fiscal year.

Rep. William H. Natcher (D-Ky.), chairman of the labor-health subcommittee, said the bill is about $5 million under President Carter's budget request and the House budget resolution for those programs.

The subcommittee stayed under its ceilings by cutting some administration requests, increasing other and shifting still other amounts.

Among the programs cut was low-income energy assistance, which, at $1.8 billion, is $400 million less than the administration sought. The aid goes to the elderly and poor through state grants and Social Security payments to help them meet rising fuel bills.

Lingering northern unhappiness over the Long formula broke into the open when Rep. Bill Alexander (D-Ark.) proposed adding $88 million in state block grants to provide summer cooling assistance.

Conte, Natcher and Rep. David R. Obey (D-Wis.), who wrote the revised formula, argued that states such as Arkansas would get more money next year and could use it for cooling assistance if they choose.

"You're callous," Alexander said, noting that his state recorded more than 100 deaths during the recent heatwave, most of them low-income persons who could not afford increased energy costs of cooling.

"The people who run your program are callous," Conte responded. "We're giving your state 24 percent more money than you have this year under this new formula."

Among the states which would lose under the committee's formula is Louisiana, which Conte said has had a 500 percent increase after Long revised the fuel aid system that had been in effect.