FOR THE Carter administration, probably the most important senator in the group that traveled to Moscow last month was Sam Nunn (D-Ga.), an expert on military affairs who could prove to be a crucial figure in the Senate debate on a new strategic arms agreement with the Soviet Union.

Nunn is known to Senate colleagues as a hard-working, moderate man who has mastered many of the intricacies of defense strategy and nuclear armaments. Carter administration officials privately say Nunn's support will be vital if the Senate is to approve SALT II.

Nunn found his first visit to Russia a fascinating experience. "I have a great deal more sympathy now" for the American officials who regularly negotiate with the Soviets, Nunn said. "It's hard to put up with all that propaganda."

Only once did Nunn have a conversation with a Soviet official unencumbered by propaganda, he said, and it may have been the most interesting exchange between a senator and a Russian in the entire visit. This was a talk Nunn had for two hours with Col. Gen. Mikhail Kozlov, deputy chief of the Soviet general staff.

It was not an easy meeting to arrange. During the week the senators were in Moscow, Nunn asked repeatedly if his previously expressed request to talk with a senior military official would be granted. Only at the last moment was it arranged, and then only because Nunn forced the issue with Gen. Kozlov directly.

"He was much more diplomatic than the politicians we met," Nunn said of Gen. Kozlov. "He knew how to get his point across without being abrasive. He didn't need a lot of propaganda-he relied on facts."

Until he had this chance to sit down with a Soviet general, Nunn said, he had been frustrated by the unwillingness of civilian officials to engage in a substantive discussion about SALT.

Nunn concluded that even senior civilian officials and members of the ruling Politburo knew little about the actual details of SALT. "Probably the most vivid impression I had on the whole trip," Nunn said, was the way the Soviets seem to "compartmentalize" information, denying it to anyone who does not have an immediate "need to know."

A high official-Nunn declined to name him-responsible for a large geographic area told Nunn flatly that there were no chemical weapons in that area, but Nunn said he knew with certainty from U.S. intelligence sources that this was untrue. Later he complained to another senior Soviet official that he had been misled, but this second man said his colleague simply didn't know what he was talking about.

Nunn said he hoped the Senate would realize that SALT II in itself could not be a very significant arms control agreement, but that the long-range process of arms control negotiations with the Russians was important. "I have really sensed the fact that the Soviet people want peace," Nunn said, citing this as the basis for a modest new hope for the longer term in Soviet-American relations.

"But I come away more apprehensive in the short term," Nunn added, "because it's obvious to me that only a few people will make the the decisions between war and peace," despite popular feelings.

Nunn said he feels military and intelligence officials from both countries should engage in regular exchanges in the future as a complement to exchanges between politicians. This could ease the impact of future misunderstandings or tension, he said.

"We're in for a long, long, tedious relationship with the Soviet Union, Nunn observed.