Definitely maybe. I'm going to take this from the American side and leave the Soviet side to someone else.

The origins of the Cold War and the nature of the Cold War remain a contested area. I know this isn't your major question, but a brief review sets the stage. The "orthodox" school put the blame for the start of the Cold War on Soviet aggressiveness. Thereafter the "revisionists" of the new left attributed the Cold War to American imperialism and the threat this posed to genuine Soviet security interests. The "post-revisionists" came along led to argue that both sides had to share blame. It's worth noting that John Lewis Gaddis, one of the leading neo-revisionists, later (in We Now Know) shifted more of the blame back onto the Soviets. Operating mostly within the field of IR rather than history, neorealists put the blame on neither side, arguing that a clash between the two leading powers was inevitable regardless of the specifics of either side's policy (see, for example, Gaddis "The Emerging Post-Revisionist Synthesis on the Origins of the Cold War" and Kydd, Trust and Mistrust in International Relations)

The point here is that allocating responsibility between the sides is challenging so allocating responsibility within them will also be hard. It's certainly fair to say that relevant players worried about the effects of military influence in government. Eisenhower in his farewell address famously warned against the influence of the "military-industrial complex." The actual issue is a bit more complex.

The implicit premise in worrying that military influence translates into a more aggressive or confrontational policy is that military officers are more hawkish that their civilian counterparts but neither the military nor civilians are a monolith and there are good arguments for military dovishness in the abstract. After all, it is the military that most directly pay the costs of war. You can definitely find isolated incidents where the influence of particular military officers went in either direction and further cases where the military was not very influential in policymaking.

Walter Poole's "From Conciliation to Containment: The Joint Chiefs of Staff and the Coming of the Cold War, 1945-1946" sketches the basic terrain of the military's view as an institution. His basic argument is that the JCS shifted from a cooperative attitudes towards the Soviets during the war to a confrontational one as the war ended and that this shift from the military came slightly more quickly than shifts in the State Department. In 1944, for example, the Joint Chiefs feared a later UK-USSR clash and counseled that the US should mediate such a dispute. In early 1945, they counseled that the Soviets would need years to recover after the end of the war and would not pose a threat to the US. By October of 1945, however, the JCS were reporting that they saw the Soviets as aggressive and that the U.S needed to begin military planning for countering Soviet aggression. Poole argues that the State Department was taking a more dovish position at this time. In February 1946, the JCS reported that the Soviets represented "the greatest threat to the United States in the near future" and had begun moving towards containment. Poole nonetheless characterizes the attitude of the military as defensive in nature -- that rather than taking an aggressive view themselves the JCS were reacting to Soviet aggression.

Setting aside the various debates on Truman, it's fair to say that the general attitude inside the U.S. government moved from a debate over post-war relations with the USSR during WWII towards an anti-Soviet consensus by 1946/1947. Here, one of the best treatments is The Diplomacy of Silence by Hugh De Santis who argues that the various factions in the State Department had consolidated towards a view of "realistic confrontation" having felt very optimistic towards the USSR as late as 1944. That is, the basic evolution is the same as the JCS even if, as Poole is claiming, it was ever so slightly slower.

The gist of this, I think, is that it may not have mattered much who had influence because the military and civilian views were not particularly out of step. The military also went along with a prevailing strategic conception in the earliest post-war years that de-prioritized military power in favor of economic power in responding to the Soviets. See "The American Conception of National Security and the Beginnings of the Cold War, 1945-48" by Melvyn Leffler and also the response by Gaddis.

In short, it's hard to escape the sense that particular military figures like MacArthur exerted a hawkish influence (as became evident in the final Truman-MacArthur showdown) but the overall thrust of military influence was not out of sync with what was coming from the civilian side of the foreign policy establishment. It's very hard to argue that the military guided policy in a direction it would not otherwise have gone as a whole.

For Zhukov specifically, this old response of mine might be of interest.