Italian Foreign Minister Emilio Colombo began his four-day Washington goodwill mission yesterday with a visit to the secretary of state and later a toney duck dinner that turned into an Italian lovefest. Even the wet March winds couldn't keep Washington's finest away.

Italian Ambassador Rinaldo Petrignani threw open the doors to Firenze House last night to welcome Colombo, who in the next few days will also meet with President Reagan and Vice President Bush. Top on his agenda is the issue of Euromissiles that are scheduled to be built in Italy this year unless the Geneva arms talks produce an East-West arms limitation agreement. Another priority is the withdrawal of Italian and American troops from Lebanon.

"Our talks were very interesting," said Colombo of his meeting with Secretary of State George P. Shultz. "East-West relations and a solution to the Mideast problem were discussed at length."

Colombo also noted through an interpreter that the 22-month-old investigation into the shooting of Pope John Paul II and the alleged Bulgarian connection was still under way. "It is the responsibility of the magistrate, and as far as the government is concerned we are waiting to see the results of their investigation," said Colombo. "Then, if necessary, we will draw political conclusions about relations with Bulgaria."

The evening began rainy and cold at the opulent Northwest mansion, which was once the Guggenheim estate. The guest list was dotted with members of the Senate Foreign Relations Committee, administration officials and others from political Washington. Among those popping roasted almonds and smoked salmon were Agriculture Secretary John Block, Commerce Secretary Malcolm Baldrige, Senate Foreign Relations Committee chairman Charles Percy (R-Ill.), journalist and socialite Nancy Dickerson and Elliot Richardson, former Secretary of Everything under Everyone.

"On the question of NATO, Italy has given us their unqualified support . . . there has never been a serious question raised about their support of the missile situation," said Sen. Charles McC. Mathias (R-Md.), a member of the Senate Foreign Relations Committee.

"Italy is very important to our foreign policy," said Sen. Richard Lugar (R-Ind.), also a member of the committee. "They agreed to the missiles . . . and then gave extra support when they came to the rescue of General Dozier. They showed great internal strength and security when it came to us--regardless of what their domestic situation might be."

Soon it was time for dinner, served in a room ready for spring: baby pink carnations and green lace cloths. But Charlene Lugar, wife of the senator, just couldn't make this one. She was snowed in in the Denver airport all weekend and had just gotten back into town. Besides, there was one other problem.

"It's Tuesday," said the senator. "It's her bowling night."