While people have already mentioned that there are in fact the necessary conditions for snow in Mesoamerica and the Andean areas, there is another form of ice far more common in the latitudes closer to the tropics, sleet or hail. At least for Mesoamerica, which is the area I study, hail is a somewhat common phenomenon during the rainy season. In fact, in some instances precipitation of hail are so high that it causes crop damage. For the Mixtecs it was called “nituhuu”; for the Mixes it is “tëtstuu”; for the Zapotecs it was “yej”. In terms of writing, in some of the colonial calendars, like in the Codex Aubin, there are mentions of specific years in which hail became such a prominent problem for some areas that they lost all of their crops.

You are wrong in your assumption that South America has no ice naturally. There are plenty of mountains and land south enough to have cold enough weather to form snow.

Here is a news piece on a "Frozen inca mummy going on display", for example

I wouldn't be surprised if a smaller tribe from somewhere warmer than the Andes didn't know about ice, tho.

The three cultures you mention lived in close proximity to what is known as the Pacific "Ring of Fire," a roughly circular pattern of earthquakes, volcanos, and other seismic activity caused by the interactions of tectonic plates. As such, there are a high number of mountainous regions nearby.

The area in which the Mayan civilizations dwelled is fairly flat and low-elevation by comparison, but parts of Maya Mountains in Guatemala rarely receive light snowfall.

The Inca civilizations lived alongside the Andes mountain range, with the primary capital of Cusco located in what is now Peru. As such, the frozen peaks of the Andes would have been quite known to them.

The tallest mountain in Mexico, Pico de Orizaba, is located just to the north of the territory of the Aztec Triple Alliance and has a snow & ice covered peak. The Aztec capital of Tenochtitlan, now Mexico City, is located at a very high elevation and numerous mountains are visible from the city, including Iztaccihuatl, which experiences significant snowfall during the winter.

As for written accounts by the people themselves, I cannot answer in that regard.

Are you asking whether they knew if ice existed?

Ice exists anywhere there is water under 32F. The Incans had access to plenty of snow and ice in the Andes mountains.