In the Soviet Union's frost belt, the heritage of old Russia survives

Acrumbling 17th-century house where Peter the Great once lived stares through broken-window eyes at icebound boats in the river below. Vologda, up here about a third of the way from Moscow to the Arctic Circle, might as well do the same.

This city, not mentioned in most tourist books and well off the beaten track, is typical of many of the neglected cities in Russia's European north.

The Soviet Union had a ''frost belt'' long before the term came into vogue in the United States. It girdles aging industrial cities, textile centers, and declining river ports. Like their counterparts in the US, these cities lose favor as more and more development takes place in warmer southern climes.

But there is an obverse side to that: Here in the cold of the north, a rich heritage harking back to old Russia survives. It takes the form of hundreds of historic churches, monasteries, and archaeological sites.

Still, the shift in regional economic fortunes may even threaten part of that legacy. A major new irrigation project will channel water from Russia's north to more temperate lands in the south, where government planners have ambitious plans to open up new lands to crops. But the plan has raised concern that some historic sites and structures may be submerged under the south-flowing waters.

Officials say they are unsure which sites in the surrounding province may be inundated. But the architectural monuments around the city of Vologda, it seems, are too far south and east to be directly under threat.

Still, even if Vologda's past is somewhat secure, its future may not be.

It remains to be seen whether any government - even one possessed of overreaching power to plan and direct the economy - can prevent the long-term decline of older industrial cities like Vologda.

A short visit here, although admittedly not providing the definitive answer, suggests that it cannot.

Fur-hatted people, their breath trailing in visible vapors behind them, board the Vologda train at Moscow's Yaroslavsky Station at 20 minutes past midnight. Nine hours later, after sleeping under freshly pressed linens, being served hot morning tea by a woman porter, they feel the sharp, chill air of Vologda.

Vologda's center has the monochromatic visage of so many Soviet cities, but here the drabness is unbroken by the showcase high-rises of Moscow or Minsk. On low, squat, precast concrete structures, the omnipresent propaganda signs - which are so often lost in the jumble of larger cities - seem to stand out.

''Lenin is with us,'' one sign proclaims about Vladimir Lenin, who died 60 years ago.

For a time his sister, Anna Ulyanova, did live here. Her home has been turned into a museum. But there is no official commemoration of another notable former resident, former Soviet dictator Joseph Stalin. Soviet officials pointedly leave his presence out of accounts of their city's history.

But revolutionists were preceded here by religionists, and they bequeathed to Vologda its most precious heritage - numerous churches, monasteries, and bell towers. In fact, the city dates its very being from the founding of a monastery here in 1147.

Perhaps the prize diadem of the city's treasures is the onion-domed Hagia Sophia Cathedral, not far from the city center. With its apses, drums, galleries , and arches, it rivals some of the churches in Moscow's Kremlin.

But next to the cathedral, an onion-domed bell tower - perhaps dating back to the 17th century - is shrouded in scaffolding. Restoration work has been under way for two years and officials can't say when the work will be completed.

Some paintings on the cathedral and outlying buildings are so badly worn that restoration is virtually impossible. And authorities have even turned one building in the Hagia Sophia complex into a base for skiers - a use that its pious builders could hardly have dreamed possible.

Meanwhile, Peter the Great's house continues to deteriorate. Large cracks cut deep into its plaster skin. Inside, a massive desk, with elaborate carved legs, draws a tarpaulin around itself, as if to ward off the damp river mists wafting through the broken windows.

The biggest problem facing restorers, says chief architect Gennady F. Shapin, of the regional restoration commission, is ''time'' - the passage of it and the effort to halt its corrosive impact.

He might have added that money isn't abundant, either. In the Vologda region, there are some 900 sites of historical interest. Yet the government sets aside only 2.5 million rubles (about $3 million) annually for historic preservation in the region.

To be sure, some progress has been made. On the outskirts of town, the Spasso-Prilutsky monastery is slowly being restored, giving visitors the chance to explore its old wooden and stone structures. Still, the elements don't stop when restoration starts: One of the monastery's buildings, restored only 25 years ago, already appears to need yet another face lift.

There is an attractive exhibit of native folkcraft and dress at the monastery. A guide, an ethnographer named Natasha, proudly points to the children's sleds, the birch-bark baskets, and the colorful wool scarfs and dresses that she says are still worn by some peasants in the rural areas.

Even in their simplicity, they far surpass some of the clothing on sale at Vologda's main department store. For 20 rubles, 20 kopecks (about $24) - a 33 percent markdown - a man can walk away with a suit made of a gray-napped fabric with prominent mustard-colored stripes. It's on display on a mannequin, which also sports a 1950s-style homburg that is several sizes too small. Even by Soviet sartorial standards, this is not dressing for success.

Still, other suits - some imported from Czechoslovakia and Finland - are in stock. So are light fixtures, cameras and photographic accessories, dishes, and a variety of other household goods.

What seems to be missing, however, is the ornate lace that has become almost synonymous with the name of Vologda for decades. Even the single souvenir shop in town doesn't have it on display. (It might have been kept behind the counter, but the shop was closed during our visit.)

When the shops close, Vologda closes, too, save for a few restaurants. The ''Sever'' (North), reputedly the best in town, serves up a zesty soup that features strong dill pickles floating in a broth thickened by sour cream.

But a request for northern Russian specialties for the main course draws a blank. If there are any regional delicacies, the natives clearly aren't telling.

It seems that, quite literally, the only hot spot in Vologda after dark is the local banya, or public bath. Inside, hearty Russians beat each other with birch leaves in a steamy half-light, chatting about weather, sports, and absent comrades.

The steam brings on thirst, and afterward, in the train station's restaurant, a waitress is asked for bottled water. It seems there is none to be had. A carbonated lemon drink will have to suffice.

The lemon drink, when it finally materializes, has somehow turned into an fizzy apple drink. But there is a problem: One bottle has a fly sealed in it.

A colleague tries a bit of levity.

''Is there,'' he asks, ''any extra charge for the fly in the bottle?''

The waitress, puzzled, holds the bottle up to the light. ''No,'' she explains matter-of-factly, the price is the same - 20 kopecks - with or without the fly.

We choose to take it without, and she provides another bottle.

There has somehow been a slip-up in our train bookings, and instead of the first-class cabin for which we've paid, we're booked in second class - with two Russians - for the return journey to Moscow.

The banter begins as the train pulls out. What did we think of our visit to Vologda, one man asks hopefully.

Before either of the two foreigners can answer, the other Russian interjects, ''It's a dirty city.''

There is a moment of embarrassed silence at the tactless reply.

But, it turns out, Vologda's critic is from the south, and so feels perfectly justified in heaping abuse on this city of the north. It's much better in the south, he boasts.

As he talks on, the train picks up speed, and Vologda is left behind in the cold, enveloping darkness.