Suppose the cold war hadn't ended. Would the United States and the Soviet Union have been able to find common ground in the fight against global warming, or would cold war politics have prevented cooperation?
With regards to the rhetoric, I would rather expect a situation like that between the US and China today. On the one side, the US blames the dirty commies for the bulk of the problem and as an excuse for why the US should not reduce emissions (since it would "make no difference"). Maybe the right of US politics would embrace global warming more and use it as a stick to beat the Soviets with? Or possibly they just say that American environmentalists are just a Communist fifth column.
On the other side, the Soviets do much the same thing - blame the capitalist powers for the problem. (As they were doing with the ozone hole.)
It would be nice to think that a continuing cold war might lead to both superpowers competing to lead the world in cutting CO2 emissions, but I rather doubt things would play out that way. Cutting emissions of CO2 is against the short-term interests of both.
That said, I think the rise of environmentalist politics in both superpowers was inevitable. Indeed, I think environmentalism would be stronger in a surviving Soviet Union.
As far as the practical effects, that depends on exactly how the Soviet Union and the world economy evolves.
OTL's economic collapse meant that the whole Soviet bloc became much less carbon intensive (and much, much poorer). It also led to population collapse. If the Soviet Union avoids the economic collapse, then not only is it likely that the carbon released per capita continues rising, the population of the Soviet Union is also likely to continue to rise.
If we assume that the Soviets converge with Canada's per capita emissions and experience population growth broadly similar to that of the USA (with children born/woman being higher in the USSR and immigration being lower) then the Soviet Union as of 2015 would have a population of around 400 million people, a per capita emission rate of 4.5 tonnes per person per year giving a total emission rate of 1800000000 tonnes of carbon per year. That's about 60% above their OTL peak and 260% higher than the Russian Federation's emission rate. That's enough to make the USSR the second largest carbon emitter after China.
Which would give some credence to the idea that Communism was destroying the world.
Of course, we could also see a situation where the Soviets survive by making their economy more efficient resulting in their emissions rate being basically flat but the quality of the goods and services they were producing rising. In that case, the Soviets would only be the 3rd largest emitter, after the USA.
Either way, the world would have less time to adapt to the problem of global warming. Expect 1 in 1000 year bad weather events to come sooner and closer together as compared to OTL.
Sources:
http://cdiac.ornl.gov/trends/emis/uss.html
http://cdiac.ornl.gov/trends/emis/can.html
http://cdiac.ornl.gov/trends/emis/top2011.tot
https://en.wikipedia.org/wiki/Demographics_of_the_Soviet_Union
https://en.wikipedia.org/wiki/Demographics_of_the_United_States
Call me Mr Cynical, but the Soviet Union couldn't even stop the effective destruction through incompetence of the Aral Sea. It would take some butt-kicking on Gorby's part to do anything effective on global warming.
The more I read about Gorbachev, the more I am of the opinion that the Soviet Union could not, under any circumstances, survive him. As such, I think it would be someone else doing the butt-kicking.
Also, the destruction of the Aral Sea is mostly an artifact of Soviet collapse. If the Soviet Union had survived to implement the measures they were starting to take at the end of the 80s, then the Aral Sea would have stopped shrinking much earlier (mid 90s from the estimates I've read). Because of the Soviet collapse, the Aral Sea became an example of the tragedy of the commons, as the post-Soviet countries who could do the most to reverse the sea's decline were the ones least effected by the problems the decline caused. Also, the post-Soviet countries in question were the very poorest - they couldn't afford to stop growing so much cotton.
fasquardon