Despite the gray skies and frequent rains of the Roman winter, the tour buses are already here, their giant hulks outlined against the Roman Forum or clogging the narrow central streets leading to the Trevi fountain.

But it is only a taste of what is to come. Normally, the bulk of foreign tourists arrives here during the summer months, leaving Italy's $21 billion of hotel facilities largely unused for most of the year. And given the relatively good buy that Italy still presents, the new low air fares between the United States and Europe are expected to give the influx a further boost.

Italian tourism, now once again inching toward second place on the world roster in terms of yearly overnight stays in hotels by foreigners, has been growing at the rate of about 3.5 percent a year.

Although hotel-restaurant prices are running 10-12 percent above 1978, bookings in the Italian South are now running at 20 percent over last year, and those in Trento, the Veneto and Emilia-Romagna at a 15-percent increase. Thus, prospects look pretty good for a country which last year earned some 5,000 billion lire (about $6 billion) from tourism in foreign exchange.

To meet this year's demand, tourist officials are urging foreigners to visit here during the months of May, June, September and October, to avoid the crush in hotels, transport and museums typical of July and August.

And they are making sure that there will be increased boat connections with the islands, better water purification plants along coastal areas like that of Emilia-Romagna, bigger fleets for car rental agencies, and a new "drive and sail" car rental program organized by the Italian Automobile Club.

A new interesting development in tourism here is also being organized by the "Agritourist" organization in Rome. They have found an enthusiastic response by setting up countryhouse rentals for those tourists who would prefer this kind of a sojourn to the urban-hotel variety.

The outlook, then, is a fairly optimistic one, since last year the number of foreigners entering Italy rose by 4.7 percent to 34.7 million. But there are some causes of worry. Between January and September of 1978, tourism from the United States dropped by 7.8 percent, reducing the U.S. share of the Italian market to 4.2 in comparison to 6.7 only a few years ago.

These figures have brought less pessimism than one would think, largely because a really serious dip in U.S. tourism last spring was ameliorated by a recovery later on.

But worry is not altogether lacking. And although tourism officials seem convinced that a part of last year's drop reflected the decline in the value abroad of the dollar (which since last spring has lost about 5 percent in purchasing power here), they admit there may be additional causes.

There is a feeling, in fact, that fear of frequent wildcat strikes, particularly in the transport sector, and ongoing terrorism could have played their part. In Rome, the only major Italian tourist city hit by scattered terrorist actions, tourism is definitely off.

The tendency of officials, however, to downplay terrorism is an understandable one. Vacation centers have never been touched, and most terrorist forays have occurred in Turin, Milan and Genoa. Furthermore, not only are such attacks sporadic and directed against Italians alone, but they involve individual shootings rather than bombings in public places in which many innocent people could be involved.

Wildcat air and train strikes are more difficult to avoid, and although no major contracts come up for renewal this year, an occasional strike -- probably of limited duration -- is certainly inevitable. Crime is also another problem. In fact, in December Italian tourism officials and operators held a conference in Rimini on "Tourism and Criminality."

Nevertheless, the situation appears stable. For although last year 54 percent of the 4,800 "welfare and whereabouts" cases handled by the U.S. Consulate in Rome involved stolen items (and 1,000 stolen passports had to be replaced), these figures represent a slight decline over those of 1977.

Furthermore, says a longtime resident of Rome, the risk of pickpockets and of purse snatchers ("scippatori") can be avoided by being very careful. "First, bags, should be kept closed, and never hung on the chair of an outside cafe or restaurant. But, above all, keep your ears peeled for the sound of an approaching motorscooter (scippatori are often motorized), and wear your bags or cameras on the arm nearest the building line and not on that facing the street. Even better, leave your valuables and passport in the hotel and try to carry gas and credit cards in a pocket or separate shoulder purse worn across the chest."

These kind of concerns, however, appear not to have proved too damaging, and Italy is still one of the major tourist meccas in the world.

As winter trembles on the edge of spring, it is clear -- even to one who has lived here now for many years -- that there are myriad reasons to explain the Italian lure. This peninsula and its islands offer the tourist an amazing variety of both scenery and historical sights, gastronomical pleasures and shopping joys, of hotels and other accommodations for almost every income, and a vast network of autostrade and highways that can really make car travel "a moveable feast."

For those who love the mountains, there are lofty peaks for summer climbing or winter skiing; for those who love the country there are rolling hills dotted with ancient castles and excellent restaurants; for those who, like myself, adore the sun there are miles and miles of gorgeous coastlines, beaches of every type and enough raw natural beauty to thrill even the most experienced of world travelers.