<----- voted for Reagan in 1980, but not a revisionist either.
He was President when it happened, but the CIA predicted the end of the Soviet Union(at least its' inability to sustain the Cold War)way back in the '60's. So, maybe, he likely just accelerated the process.
Perestroika is seen by many as instrumental in the Soviet economic collapse. While their economy wasn't growing, it certainly wasn't at crises stage when Gorbachev took over. The CIA began reporting on declining Soviet growth rates in the 1960s. Once Gorbi entered the equation, analysts at the CIA were able to further refine their estimates.
Some historians think that the decline in the Soviet economy actually began during the 1970s under Brezhnev. Brezhnev believed that capitalism was doomed to failure. In order to hasten this "failure", he therefore escalated the arms race and Soviet influence in the Third World.
The Reagan admin had a significant influence on the "end" of the Cold War through policy. However, to say that Reagan "won" the Cold War is somewhat misleading, in my opinion. There were a couple of defining actions on his part though:
P-II and Cruise Missile deployment: The 230 Pershing II missiles deployed to southern Germany in 1983-84 scared the living hell out of the Soviets. P-IIs, which could reach Moscow twenty minutes off the pad, definitely pushed the Soviets towards the INF. NATO originally approved the missile deployment in 1979. There were already approximately 160 P-Is in country in German and US hands prior to deployment. Incidentally, the warheads were under US control. In late 1983, despite numerous domestic protests, the Germans approved forward deployment of P-IIs on their soil. C-5 aircraft began flying the missiles to Ramstein AB for redeployment to 56 FA a few days later. During 1987, influenced by the precision accuracy of the P-II, the Soviets and the US conducted INF negotiations. In short, the Soviets backed down on this issue.
Afghanistan: This was the Soviet version of Vietnam. Unfortunately, our support of the insurgents during the early 80s came back to bite us in the ass later on. However, the spending for arming the insurgency during this period was relentless. The goal was to transform Afghanistan into a quagmire as messy as possible for the Soviets. To some degree, the strategy worked rather well.
Conventional force modernization: Many of the conventional force improvements had already been developed prior to Reagan entering office. At any rate, Reagan accelerated defense spending. This increased spending produced dramatic improvements during the 80s thereby resulting in a force that could actually fight and win.
Grenada, 1983: This sent a huge message to Castro, the Soviets and the American people. We were tired of defeat. Two days before this invasion, the USMC barracks in Lebanon was bombed, killing 241 Marines. We desperately required an event to strengthen our confidence and demonstrate our resolve. The success of the operation in Grenada provided both.