Well, Civ 2 did not really make use of ICBMs (Intercontinental Ballistic Missles). Instead Civ 2 mostly used tactical nukes or nukes you specifically tell what to do each turn, and there was also the ability to place a nuke using a spy. But the real fear comes from ICBMs.
I suggested adding an ICBM unit to civ 2.
Here's how it would work:
Assign it a target.
The ICBM would have a command allowing you to assign a specific tile for it to attack. It would then retain this tile in memory till your ready to use it.
Nuclear War
Somewhere in Civ 2 there should be a command to allow you to lauch your ICBM's at this point all your ICBMs that you designated a target for would be launched. This is where the cold war idea comes in. All other Civs would have the option to launch their preset ICBMs as well before your turn is over. Thus, things would take on a true nuclear war with all sides incurring casualties.
Give it 0 movement points
Since the ICBM is not a regular unit, it has no movement points. To load it into a submarine you would move the sub into the city and load it on (like you can in Civ 2). To move to another city, there should be a unit that can do the same thing -- as well as an aircraft that can transport them as well).
Attack Order
There should be an order where you can tell a single ICBM to attack a location on the map instead of having to launch all your preset ICBMs. The enemy would of course detect it and have the option to retalitate with all their forces of ICBMs before your turn is over.
Missle Silos
Using your worker units you should be able to build silos anywhere you want and thus transport ICBMs to them for keeping till you use them (if ever).
Other Nuke Options
1. There would still be the regular old nukes in Civ 3 like there was in Civ 2 -- nukes that have move points as well as using nukes via a spy.
2. Thes other nukes cannot be detected upon launch or anything because they're not big and noticeable like ICBMs. However, once you hit a civ with one of these alternative nukes, the enemy should have an option to strike you with their ICBM arsinal before the turn is over (and of course you can respond in the same as can other civs). Thus, this would deter you from even using other types of nukes.
3. When a spy hits a city with a nuke, there should be a chance that the other civ did not detect your spy and thus cannot tell who did it.
Neutron Bomb
The neutron bomb would be a nice third type of nuclear weapon (perhaps in regular form AND ICBM form). The neutron bomb just kills lifeforms, but doesn't touch structures.

Options
Any time the message pops up asking if you want to launch your ICBM arsenal, you should also have a list of check boxes for the countries you want to attack. For example if you have some ICBMs targeted at Russia and some targeted at China, you can just put a check beside Russia to have those targeted at Russia to fire.

So, as you can see, basically the idea is to have a true cold war kind of feel with nuclear weapons and the result of using them can have drastic consequences.