Cowboys, Mexicans and oilmen make Texas the most culturally distinctive of the major states. But the political heart of Texas lies in the most nationally homogenized of all American communities -- the suburbs. iWhich is a main reason why winning the crucial battle for this state's 26 electoral votes is an up hill struggle for Jimmy Carter.

Suburbanites in Texas make up nearly 30 percent of the voting population. That is far more than either of the big minority groups -- blacks with 12 percent and Hispanics with 18 percent. The figure probably exceeds the rural vote. Moreover, the suburban vote continues to grow as the center cities level off. Arlington, Irving, Euless, Bedford, Hurst, Grand Prairie and Plano -- the suburbs here in the Fort Worth-Dallas area are still burgeoning.

Similarities between the suburbs in Texas and those everywhere else abound. Suburbanites here depend upon their cars and do most of their buying at shopping malls. They work for national companies in white-collar jobs that require more than a high school education. They provide the big support for the local ball teams -- which are in the big leagues. They take their news, and not a little of their life style, from the national media. They even poke fun at J. R. Ewing.

But far more than most suburbs, however, the Texas suburbs work. This is still a land of wide-open spaces, and though there are complaints of congestion, especially in Houston, they don't ring true for anybody who has had to fight the traffic outside New York, Chicago and Los Angeles. During the morning and afternoon rush hours the other day, I drove first from the airport to Dallas, and then from Dallas to Fort Worth, without running into traffic tie-ups.

The big companies -- for example, American Airlines, which has just moved its national headquarters here -- are still expanding in the area. Thus, the recession has hardly made itself felt. "It's something we read about in The Wall Street Journal," one local businessman put it.

Not surprisingly, the mood here is upbeat. "Growth" is not a dirty word and "progress" is not a term of irony. North Dallas and West Houston -- the two major suburban areas of the state -- are among the very few districts in the country where voterturnout has been rising.

With local communities functioning, and business thriving, and morale high, people here have the quaint conceit that government should work too. There is very little sympathy for Jimmy Carter as a nice man who tries hard. tOn the contrary, the competence issue works strongly against him. "Carter has to prove," says Jess Hay, a Dallas mortgage banker and close supporter of the president, "that he runs a competent administration."

Proving that point is not going to be easy for the Democrats in Texas this year. For one thing, moderate Democrats who cammand broad respect in suburban areas seem to be taking their distances from the president. rSen. Lloyd Bentsen, the suave heir to a real estate fortune who made his own fortune as an insurance executive, is honorary chairman of the Carter-Mondale committee in Texas. But the emphasis seems to be on honorary.

Dolph Briscoe, the former governor who helped Carter carry Texas in 1976, seems mute this year. Jim Wright, the House Majority leader, has his hands full in Fort Worth with a conservative opponent, Jim Bradshaw, who is backed by the evangelical group known as the Moral Majority. For the main speaker at a fund-raising dinner here in Fort Worth last week, Wright called on the chief Watergate prosecutor, Leon Jaworski. Jaworski is not only supporting Gov. Reagan, but he got a big hand at the dinner when he referred to President Carter as "lamentable."

Democratic weakness in the Texas suburbs is matched by Republican strength. George Bush, Reagan's running mate, and former Gov. John Connally both live in West Houston. William P. Clements, the first Republican to become governor of the state in a hundred years, won by a heavy concentration of media advertising and phone bank operations in the suburban areas. He has raised about $3 million for the Reagan-Bush ticket, and is once again setting up a bank of several thousand phones.

Jimmy Carter can still win even if the Texas suburbs go heavily for Ronald Reagan. But he has to draw a huge turnout in three groups that are now both at odds with each other and badly dispirited -- rural whites, Hispanics and blacks.