Their R-7 didn't have the range to hit NY
One of the reasons they wanted missiles in Cuba, as just being able to destroy Seattle or Bangor, and other far north cities wasn't enough to deter the USA
The R-16 certainly did though, and that represented the majority of deployed Soviet ICBM strength in Oct 1962. Very vulnerable to a first strike though.
Really, recovery time will depend on how the exchange goes down. USSR and Europe destroyed regardless, China probably but not necessarily heavily damaged. USA with 5-50 targets hit depending on who strikes first.
I think using the WW2 experience is flawed. Nuclear bombing is vastly more destructive from a population and physical perspective than conventional plus potential radiation effects. Also, the damage is sustained in a short period of time which magnifies the economic and societal disruption.
There will be climatic effects after an exchange of this magnitude - the original 1986 study may have been a bit off the mark but the using current climate models and a "small" exchange (India-Pakistan, 100 weapons) there was significant global cooling. It wouldn't be world-ending but shortened growing seasons added to disruption in agricultural and transport infrastructure and you're likely seeing famines for at least the first couple years post-exchange.
All in all, best case scenario (US first strike) you're looking at progress being set back at least 25 years. Worst case, more like a century. Agree that '62 exchange would be much better for humanity than an '83 one, where you're basically looking at the collapse of industrial civilization in the Northern Hemisphere at the very least and most probably much worse than that.