So just some historical footnotes with regard to this: First, Continuity of Government (COG) on the United States side was believed to be compromised by a spy in the FBI at this point in our history, so any precautions to protect vital government officials would not function.
Second, I'm concerned about your order of battle (though the delayed retaliation from the Soviet's would be due to the fuel concerns. Soviet Missals historically would have taken longer to fuel up, but given a slow progression to war, it would have probably been fueled. Also, the Soviets always had a policy of Second Strike Only (i.e. We will not use nukes first) where as the U.S. did have an unstated point of First Strike (never outlined on policy, but up to the option of POTUS). The Germany "Fulda Gap" was always a ruse on the Soviet's Part which the United States bought hook line and sinker. The United States at this time was currently revising policy of it's first strike. Again, it was never a labeled event, but the general "We're losing" was a good point. The idea of tactical nukes was very recent (the 80s) and even then, the lead time of a first strike meant that it was better for a First Strike opponent to launch all nukes upon the decision to launch one (during the entirety of the cold war, it was thought that only 3% of all nukes would reach their intended targets, so getting everything out of the ground in the mother of all salvos was the best strategy... not limited detonation on troops and military targets, because that gave the enemy time to get their nukes off the ground. In the 1970s, with limited forward operating areas, a second strike policy, and the slow speed of fueling, the United States had the clear edge over Soviets in a first strike.). Given the timely nature of fueling rockets by the Soviets for a counter attack, the first indication that this process was starting would be enough to call in an all out nuclear strike from NATO forces... lest those missals get off the ground.
Another wonderful historical fact is that the Soviet Government did not tell the populace about radiation and its harmful effects, so it's likely at local levels, the rebuild plan would have been significantly hampered. Since most of the Soviet's population was in the Western part of the country, it's likely that Asiatic Russia would have seen little of the war, though this could change due to the fact that all Soviet Nukes were mobile (due to the fueling) and not siloed like in the states, which had a good chunk of nukes in the breadbasket... in the event Soviet Union could launch a Second Strike, a good deal of the American Bread Basket would have been highly irradiated. When the US did nuke Japan, Tokyo was deliberately not named as a candidate city because they needed people to negotiate a surrender with. This may preserve the capitols, but it's likely not.
In short, the United States would likely have been better prepaired for the aftermath, but famine would be an immediate scare for the survivors and hospitals would be overwhelmed... a single high atmosphere detonation would cause an EMP that would fry all electronics in the Continental United States, so power infrastructure would be need to be rebuilt. In the Soviet Union, the problem is that the Government would have probably not briefed the local leadership on what to do in the event they survive. Radiation poisoning would probably be much more rampart among the survivors. Foreign Aid would probably be more readily given to the United States (China had long had a bitter falling out with the Soviets... during this time period, they may have even launched on the Soviets for good measure, leaving the Soviet Union with little in the way of actual allies who could give back.).
For some good documentaries/fiction that generally got a good portrayal of what you want, check out "The Day After" which focuses more on the survival of the initial strike than the build up (to hit the point home that it would be the case in any direct nuclear war, who started firing the nukes was never explained... the viewer can blame the US and USSR equally), "Gerico" (this was co-ordianted domestic Nuclear Terrorism in the the 00s but still showed several hardships the town would face if major cities were wiped off of the map). I've heard good things about "Threads" (but never saw it) which is the UK version of "The Day After" and much much darker... and even "The Day After" admitted it was toning down the realistic consequences because there are somethings you can't show on TV.
TVTropes.org has a good description of what would happen if someone who really... really... really hated Mickey Mouse detonated a low yield Nuclear device at the Walt Disney Studios in L.A. "War Games" is actually considered "scary accurate" for it's depiction of build up to Nuclear War (especially given that there are more than a few incidents that almost sparked a nuclear war that read scary close... including an incident in the Soviet Union in the same year the movie was released). "Deuscthland 83" is a good depiction of the fears from both side of the Iron Curtain and depicts the reasons behind the real life Able Archer '83 scare from the Soviet's perspective (it's subtitled from it's original German language release on Hulu, but don't let that stop you... the 80s soundtrack is awesome!).
Edit: To clarify some comment confusion. Russian military terminology is extremely nuanced and well defined, so that understanding the definition of the terms in question means exactly that thing and is not interchangable for political reasons (in the United States, First Strike and Pre-Emptive strike are kinda the same thing. In Russian military, they do have specific meanings and are not interchangable).
With that in mind, a second strike is what it is: They Launched Nukes, we got to fire back before we have none.
A first Strike is "We launched nukes as an opening action to war.
A Pre-Emptive Strike is "We're launching first because it's pretty obvious they're going to launch anyway if we don't do something".
A Pre-Emptive Strike was accepted as a second strike because the gun was drawn and cocked first by the enemy... we just fired quicker than them.
The silliness of this idea was the subject of the a popular Russian joke in which, having watched two other foreign-nationals die at the hands of a cannibal chief without intervention, the Russian tricks the chief into picking up a gun and promptly killed the chief because now the Russian couldn't be seen as the aggressor.
To the Soviet's mind, of the two great superpowers, only one actually used Nuclear weapons in actual combat... not only was leadership terrified that the U.S. would use nukes first, but they could point to a historical moral high ground. For it's entire history as a Nuclear Power, the Soviet Union only had them as a means of self-defense.
Of course, in order to use Nukes as self-defense, you had to show your enemies that you're just crazy enough to kill everyone on the planet if provoked, so you had to show that there would be a line in the sand where you would invoke Mutually Assured Destruction. SF-Debris, in his review of "The Day After" explains this pretty well... and Yes Prime Minister shows the consequences of politics under these pressures in what it called "Salami Tactics" (you wouldn't push the button on small scale pushes... it was kind of like two children in a car playing the most dangerous version of "I'm not Touching You" ever.). "Deustchland 83" even shows how, in an effort to suck up to the Soviets, the East Germans made it look like the United States was more willing to strike first than they actually were... and that misunderstanding was enough to lead to the very real Able Archer '83 panic that the Soviet Leadership went through.