The United States certainly did not in the early Cold War, and as far as I am aware, not for the rest of the Cold War, either.

For reference, I define the early Cold War as from 1945 to 1962, the period during which bombers represented the biggest strategic threat against the United States. From 1963 onward, the missile surpassed the bomber as the principle threat against the United States, and planning for civil defense and recovery shows a marked difference between the two periods. The difference between several hours of warning and 15 minutes led to some degree of fatalism in the United States and the rest of the Western nations with regard to nuclear warfare. Only in the early 1980s did this belief change somewhat (and by the later 1980s die away again).

In any event, during the early Cold War, the focus was on survival plans and civil defense. It was believed that the principal and most difficult mission was to simply survive the initial exchange of weapons, and that fighting would not last long (if at all) after this exchange. By the late 1950s, however, the United States did have a Strategic and Critical Materials Stockpile. President Kennedy's committee on this stockpile declared in March 1962 that "the requirements of limited war shall continue to be the objectives of the stockpile, and a study shall be made of the proper scope of stockpile objectives for general nuclear war and the extent of stockpile necessary for the reconstruction period."

The stockpile was intended to "(meet) the estimated shortages of materials for a three-year emergency." This might include a limited war after the initial exchange, or simple recovery after the fact. In March 1962, the stockpile included more than $7.7 billion worth of material (1962 prices), which was no small amount. It consisted of critical raw materials and minerals, but it did not consist of significant stocks of food or other perishable consumables. Moreover, there were no concrete plans for the use of the stockpile.

At the time, there was extensive lobbying from the Left against the idea of civil defense and recovery plans. The thought was that civil defense planning made war more likely because it fostered the idea that nuclear war was a survivable thing. If it was a survivable thing, there might be the idea that a nuclear war was winnable. Articles in The Nation, The Atlantic and other, similar newsmagazines and publications attempted to poke holes in the idea of civil defense, but the idea was popular enough that even Kennedy (hardly a right-winger) pushed civil defense and shelter programs once elected to office. His push (and that of Truman and Eisenhower) was largely limited to shelters and supply stockpiles, however.