Tourists in Miami wore earmuffs on the beach, tenants in New York launched a rent strike to get landlords to turn up the heat, and even the tough breed of New Englanders who man the lobster boats surrendered to the weather yesterday as the stinging winter of '81 continued to break low-temperature records along the length of the Eastern Seaboard.

The persistent rush of Canadian air that has swept the eastern third of the United States since Christmas led to temporary blackouts and fuel shortages and threatened to reduce supplies of commodities ranging from seafood to citrus fruit. Forecasters predicted the cold front, swirling in a counterclockwise whirlwind reaching from Quebec to south Florida, will continue at least through the weekend.

The temperature registered 43 below zero at Old Forge, N.Y., yesterday; record lows were also reported at Warwisk, R.I. (8 below); Pittsburgh (5 below); Philadelphia (3); Baltimore (1); Columbus, Ga. (16), and Greensboro, N.C. (2).

That made Florida's records -- 22 at Crestview, in the panhandle; 38 at Miami Beach -- seem almost toasty by comparison. But representatives of the state's two big winter industries, citrus and tourism, were concerned that the cold -- the worst since a mid-January freeze four years ago -- might have lasting economic effects.

Orchard keepers set out smoke pots last night and hoped that temperatures would not reach the 28-degree point at which oranges, tangerines and grapefruit start to suffer frost damage.

Ray Sforza, chief of Miami Beache's lifeguards, said yesterday that he could see "five or six people" on the famous beach. "There are a few hardy souls," he said, "with earmuffs." In Jacksonville and some other Florida cities, homeowners who rely on electric space heaters demanded so much power that utilities instituted rotating blackouts, cutting power for 15 minutes to 10,000 homes at a time.

About 1,500 miles to the north, a natural gas shortage forced schools and factories to close in southern Massachusetts. Gov. Edward J. King asked homeowners around the state who heat with gas to lower thermostats so fuel could be diverted to utilities in Lowell and on Cape Cod, where supply fell to emergency levels.

There was a threat of fuel oil shortages as well because tankers carrying crude to New England found their routes locked with ice. The Cape Cod Canal, an essential thoroughfare for Boston-bound tankers, has almost solidified.

The New England fishing industry was effectively frozen in port as harbors iced over and fierce storms at sea drove ships back home. At New Bedford, tonnage has dropped 80 percent over the past three weeks, according to Brian Veasy, executive vice president of the New Bedford Seaford Cooperative.

The wholesale price of fish, accordingly, had risen as fast as the temperature has fallen. Scallop prices at the dock are up to $6 a pound from $4 three weeks ago. Haddock and flounder prices have doubled in the past two weeks to about $1 per pound. Edward Blackmore, president of the Maine Lobsterman's Association, says his members' furloughs will result in shortages that will take lobster prices, $5 per pound last month, to about $7.

Even New England's ski industry has been hurt. With wind-chill factors of 50 below on some slopes, skiers stayed away in droves. At Waterville Valley, N.H., operators worried about frostbite refused to seel lift tickets to anyone with skin exposed to the air.

In New York City, thousands of heatless apartment dwellers swelled emergency shelters. Tenants in 20 city-owned buildings in Manhattan started withholding rents in protest.

If it is any solace, the East's biting cold follows by a few months the hottest summer on record for most of the region. The mid-Atlantic states had 60 days last summer when the temperature exceeded 90 degrees, a record. Six months ago this week, on July 16, the temperature in Washington was 103.