The United States did not treat all immigrants from Latin America in the same way. Who got treated better? Why?
I would agree that the biggest effect the Cold War had on the treatment of Latin American Immigrants was whether tey were coming from a communist led country or non-communist led country.
It made the US more aggressively interventionist in Central America, in trying to keep non-communist leaders in power, even if they were brutal dictators. This had one of the greatest effects on immigration policy where Cuba is concerned.
The Cuban Revolution in 1958 led to repeated attempts by the US to remove Fidel Castro from power, but it also led to a policy where Cubans could become legal residents of the United States without an application process - if they simply made it to US soil, we had to admit them as legal immigrants. This law is still in effect today.
The major impact of the Cold War on US foreign policy towards Central America in general was that it caused the US to help those countries that it thought were anti-communist. In addition, the US tended to try to undermine governments that were seen as communist or sympathetic to communism.
In Central America, you can see this in such actions as the US-led coup that toppled Jacobo Arbenz in Guatemala and in the support for various dictators in the region.
As far as immigration policy, the main country to be treated differently has been Cuba.
Most of the policies the US crafted during the Cold War were meant to oppose any communist regimes anywhere in the world. Their attitude towards Latin American countries was shaped by similar concerns.
Their policies towards immigrants from Latin American countries were shaped by whether or not they felt that allowing greater immigration to the US would either strengthen or weaken the anti-communist forces in those countries.
Just as the US has allowed asylum requests from certain countries in order to curry political favor amongst the elite power-brokers of those countries, they did the same in Latin America during the cold war for the same reasons.
I would disagree that immigrants from one Latin American country were treated any differently than from any other country. It is probably based on what the people brought with them to start a new life and how did they arrive in the US. Those two probably separate the attitudes of people.