From the period of 1949 to 1963, the Arms race was a period were there which saw two superpowers the USA and the USSR increasing their nuclear technology developments. The arms race ultimately prevented tensions from escalating into an actual fully fledged war. On the other hand there were de-stabilising factors that put both countries on the brink of nuclear warfare and the world at risk of annihilation, such as the pressure of domestic politics, hot wars in Korea and Vietnam, and the Cuban missile crisis. Regardless of these factors the war remained a Cold war. This is because the arms race created the most important stabilising factor which was mutually assured destruction. Both superpowers realised the devastating capability of Nuclear weapons and as a result they did not use Nuclear weapons. Therefore the arms race (and fear of the consequences of an arms race) outweighed the other de-stabilising factors to a large extent from 1949 to 1963.
An important reason why the arms race was a stabilising factor in the Cold war is because it led to Mutually Assured Destruction. This is based on the idea that the existence of massive nuclear arsenals prevented the conflict between the Soviet Union and the United States from devolving into outright war between the superpowers. The arms race helped to keep the war cold because both Kennedy and Khrushchev's administrations knew that due to the massive nuclear stockpiles on each side, outright war between the two sides would result in both sides being wiped out and the possible destruction of the world. It was clear that the nuclear arms that both powers possessed compelled the Soviets and the Americans to avoid outright military conflict. Therefore the arms race was a major stabilising factor in the Cold war.
On the other hand, the arms race could be argued to be less stable as it caused tensions to develop because both