I've read a decent amount about the Cold War. Most of what I've read seems to lend itself towards the idea that the massive amount of nuclear warheads in service for each country were mainly thought of as being used in retaliation to a nuclear strike by the other country.
What I'm saying is that I haven't read much of anything that suggests the Soviet Union or United States ever seriously considered making a first strike, or had a set plan to do it.
I know that there are several instances where nuclear war was incredibly close to happening, but I never got the feeling that it would go "It's Sunday morning here in the United States and... looks like the Soviet Union just launched all its available nukes."
As /u/the_rabbit_of_power says, the USA used to have a "tripwire" policy starting in the Eisenhower era. I think this stopped in the Kennedy period.
For later periods it's important to remember that the USA is not the only nuclear power in NATO. The UK and France (the latter not always part of NATO, but always aligned with its members) were more likely sources of a first strike. The USA was geographically isolated from the USSR and not a likely target of invasion; invasion of the USSR from Europe would be difficult and there would be little point. In contrast a massive conventional attack on Western Europe culminating in invasion would have been practical for the USSR. French and British nuclear weapons have to be interpreted in this context, where they might be used in response to a conventional attack. Note however that at least in the cast of the UK, there is a standing policy of not discussing the criteria under which nuclear weapons would be used - i.e. there is no statement on whether first strike would be used.
EDIT - apparently the tripwire policy was encoded in NATO document MC14/2, which was replaced in 1968 by document MC14/3 defining "flexible response".
Read "On Thermonuclear War" and "Thinking about the Unthinkable," both by Herman Kahn, both written in the 1960s at the height of the Cold War. Both books strongly influenced US government policy. You will be amazed, I think, and perhaps frightened, at how deeply the various strategies were thought out.
Recently release documents show that Castro had a first strike policy and planned nuclear war against the States as Russia was handing him nuclear weapons. The Soviets explained that he would suffer under a radioactive cloud and convinced him to back away from those views.
http://www.nytimes.com/2009/09/22/science/22nuke.html?_r=0
http://www2.gwu.edu/~nsarchiv/nukevault/ebb285/index.htm
It does seem that by the 60s both countries fully accepted that nuclear weapons were pretty much deterrents, not first strike weapons. The Soviets did have an official doctrine that nuclear war as survivable. I don't think the US had that. The Soviets also believed in launching a first strike under "premonition" of assuming a US strike was going to happen. Its not clear what that means and can be interpreted as first strike capabilities.
The Soviets and modern Russia today also have "limited" first strike policies that would be used on military targets if the Soviet/Russian army was to be losing. I imagine this would be low yield tactical nukes.
"if Russia were faced with a large-scale conventional attack that exceeded its capacity for defense, it might respond with a limited nuclear strike. "
http://thebulletin.org/why-russia-calls-limited-nuclear-strike-de-escalation
It should be noted that it is absolutely normal for contingency plans to exist but with really little interest in using them. Note that Churchill's Operation Unthinkable (Post WW2 attack on the USSR) never, of course, happened but it was an option on the table first for the UK and later the US. And yes, it would have gone nuclear.
Ordinary soldiers practice by marching and shooting, staff officers by planning.
Yes.
There were a number of plans that involved first strikes, both tactical and strategic first strikes.
The most accessible one is the 1979 Red Army wargame plan "Seven Days to the River Rhine".
Now Seven Days to the River Rhine predicted a NATO first strike on the Vistula river valley to disrupt the Red Army supply and reinforcement routes, but the counter-strike included RAF, Italian, USAFE bases and nuclear strikes on Vienna, Vicenza, Verona, Stuttgart, Munich, Nuremberg as well as Roskilde and Esbjerg in Denmark.
The US and Warsaw Pact also had plans for limited nuclear strikes and nuclear denial weapons in strategic places like the Fulda Gap. The US had nuclear demolition munitions there to deny a route for armor and the Warsaw Pact had plans for tactical nuclear strikes to clear the US defenses.
The UK, US and Soviets all had decapitation first strike plans for Moscow and Washington DC. Close in cruise missile or SLBM shots from submarines were American and Soviet plans, the UK was going to fly bombers in at low levels against Leningrad and Moscow's defenses to open a gap for follow on bombing of those cities.