The world's next big hot war is getting ready to happen in Ethiopia. Nominally the fighting, which promises to be long and bloody, pits the local military regime of Lt. Col. Mengistu Haile-Mariam against a powerful guerrilla movement in Eritrea.

In fact, the Russians and probably the Cubans back Mengistu, and the Ethiopians are apt to win, thus giving the communists another leg up in Africa and the Arabian penisula. America's Arab friends back the Eritreans, and they and the United States figure to take a pasting unless Washington can come up with a new policy for the Horn of Africa.

Eritrea makes up the northern part of Ethiopia. It borders on the Sudan, and gives access to the Red Sea. The Italians held it from the last century to the end of World War II, and it was accorded federal status inside Ethiopia in the postwar settlement. But in 1962 Emperor Haile Selassie simply appropriated Eritrea and its 3 million inhabitants for Ethiopia.

A low-level guerrilla operation against the Ethiopians has been in the works ever since. When the emperor was ousted in 1974, with a loss of central authority in Addis, the seccessionist movement took off. Working in conjunction with guerrillas backed by Somalia in Ethiopia's eastern province, the Ogaden, the Eritrean guerrillas took 99 percent of the territory they claimed - which meant everything except the capital, Asmara, and the Red Sea port cities of Massawa and Assab.

In the spring of last year, however, Mengistu made his Moscow connection. Thanks to Russian and Cuban help he rolled up the Somali forces in the Orgaden last month. Ever since, he has been Looking north to Eritrea.

Already the fighting has stepped up significantly. After a massive bombardment by planes, missiles and artillery, the Ethiopians attempted a foray out of Asmara on the night of April 15. The guerrillas took heavy losses, but held on. They knocked down one plane and four helicopters, and inflicted some 2,000 casualties.

The lesson of that encounter is that the Ethiopians will need Russian help. The Russians are nothing loath, but they would like to cover their role with a Cuban military presence. According to Cuban, Russian and Ethiopian diplomats, here, Fidel Castro entertains scruples about sullying Cuba's reputation of spotless revolutionary disinterest by an all-out attack on the Eritrean liberation fronts.

During the past few days he has been talking the matter over with Mengistu in Havana. The debate is apt to be intense, for Mengistu has climbed to his present eminence by ousting two former Ethiopian military leaders on the grounds they were not tough enough in dealing with Eritrea.

So the odds are that the Ethiopians and Russians will pull the Cubans in with them. Already the Cubans are placing their troops for a go at Eritrea. Similarly, the Russians are continuing a huge airlift of military equipment. At the airport yesterday, I counted a score of Antonov transports. European pilots working around the area told me they were newly arrived, and brought with them tanks and wingless jet planes, which were quickly assembled and flown off.

So all is in position for a big military push - probably before midsummer. Nobody here thinks the fight will be easy. British and Italian veterans of the area talk about years of fighting, with casualties running around 300,000 to 500,000. But nobody doubts that, in the end, the Ethiopians - who are no mean fighters themselves - stiffened by Cuban and Russian support, will prevail.

Neither does anybody doubt the Russians will then be established for years to come in this country. Nor that they will use their strong footing here to make trouble in Kenya and other African lands to the south, and possibly in Saudi Arabia across the Red Sea.

What is in doubt is the response of the United States. So far President Carter has, to an extraordinary degree, allowed Egypt and Saudi Arabia to make his policy in the Horn of Africa. He took their estimate of Somali strength at face value, and ended up supporting the wrong side there. He seems to be identifying the United States with the Eritreans - another losing cause that will only alienate Washington further from the true power in the area, Ethiopia.

At bottom the American objective is to win back from the Russians the inside track here. That will undoubtedly take years. But a good starter would be to stay away from the fighting, and to come forward with peace proposals that give a modicum of independence to the Eritreans, while assuring the Ethiopians what they, and all other African states, want: the preservation of the territorial status quo.