Hey there! First time answering here. I'm a History teacher and researcher from Argentina. The conquest and subsequent colonial period /is not/ my field of expertise, but I did take several courses on these subjects during my grad studies. Not sure if that qualifies me to try a response, but I'll give it a shot!

So, to start off, I think you're basing your question on a false premise. Vast areas in Central and South America are not in fact tropical (that's just a misconception that's been around since forever). Far from it. Many of the most heavily populated areas in Mesoamerica, like the central mexican valleys, have temperate (if somewhat humid) climate. The same can be said of southern Brazil, central Chile, modern day Uruguay and the argentinian Pampas, amongst other smaller areas. Northern Mexico, Northern Chile or Northeastern Brazil (areas occupied, if barely, by Spain and Portugal) are extremely arid, even desertic. The point I'm trying to make is that these so called "tropical areas" are not entirely so, and that most colonial settlements tended to cluster in non-tropical spaces, particularly the mountain valleys that dot the entire lenght of the continent, where most of the native civilizations developed (specially the Mexica and Incas, the Mayas not so much), and which vary greatly in climate, depending on altitude among other factors.

Spain's and Portugal's focus on areas like Central America and Northeastern Brasil had little to do with climate familiarity. As a matter of fact, no european colonial power had any sort of familiarity with growing crops in permafrost (refering to your example): that's the reason permafrost areas haven't seen permanent (as in non-nomadic) settlements until very recently in history. Rather, their push to these other areas can be explained by (amongst other factors) profitability. This is where you could grow cash crops and exotic products (sugar, cocoa, coffee) not avaliable in Europe. Even then, the greatest magnet for colonial conquest was, at least at the beginning of the whole process, the promise of gold and silver. The greatest gold and silver producing areas in Spanish and Portuguese America were not, in fact, located in tropical areas either (San Luis Potosí, Zacatecas, Minas Gerais, etc.).

So, to sum it up: despite what most people think, most of Central and South America can hardly be described as tropical. During colonial times, most of the population and economic activity was located outside tropical areas, which in fact played a marginal role in the region's history until later (17th century and onward, with the growth of sugar production as one key example). Spain's and Portugal's push to occupy these areas can most likely be explained because they held more readiliby avaliable riches to be exploited, and in some cases (like Mesoamerica and the Andean region) the manpower needed to do so. The English and French, on the other hand, joined the colonial "race" later (which is why they tried several times to wrestle control of some areas occupied by Spain and Portugal) and had to make do with the a priori marginal and unprofitable North.

/u/MrVasch already gave a great answer - I'll add a few points since I already wrote it down before seeing the other answer, less directly on climate differences (sorry for some overlaps).

We can take a few very general approaches to look at who got where first. One is the territorial division of the world in two parts, e.g. with the well-known Treaty of Tordesillas and later treaties, ratified by the pope. This meant that the (not very fixed) marcation in the Americas was roughly separating modern-day Brazil from Spanish America. For the Portuguese until then their main focus had been on their Asian colonies and the spice trade, and they only put a stronger focus on Portuguese America later on; so this fit with their plans at the time quite well.

Another point is the Spanish economic interest which has already been discussed. Basically, the early Spanish conquistadores wanted to find gold (later silver), and to gain to right to indigenous labor. With this they aimed to finance their expeditions which they usually had paid themselves; and to become rich, which only few managed to do. So going to a place with a nice climate was much less important to early colonizers than finding places with a) possible gold/silver finds and b) large enough native populations to make them work. As you know, both the Aztec and Inca states fit this pattern, which is one reason for why those conquistadors went there (with some randomness thrown in).

Seen in this way, it was also a question of simply “who was there first”. Of the course the treaties with the church and the Iberian powers played a major role – although the exact frontiers were often far from fixed, and would remain in flux into the independence period, esp. in South American regions. But for later power like France and England, who at least at first were not so powerful newcomers, it was often a question of finding a region with no prior European power there. In order to avoid difficult to win wars abroad. But also since British justification for coloniazation since John Locke built on the principle that previously “unsettled” land could be freely taken. Of course, for the British this included European but not native American states whose rights to land were simply overlooked or taken over.

To come back to your question on climate: that the Spanish usually did not feel positively about the climates in their overseas possessions is also very clear in contemporary accounts. Major debates were held over the colonial period on the “humanity” of the indigenous populations. One argument brought against both native people and criollos (Europeans born overseas) was that they were much more supposedly “lazy”, “weak”, “unproductive” or [insert other negative adjective] simply due to the hotter, often more humid American climates. This was also tied to arguments about the four humours used still in Europe.

Especially criollo elites in turn would turn around such arguments. Mexican scholars like Bernardo de Balbuena or Carlos de Siguenza y Góngora would in the 17th c. very much praise the climate of their home region. For them, the “temperate” climes of Mexico led to higher intellectual capacities – in stark contrast to what Spanish scholars argued at the time. So you can note how the differences in climate were used by both sides for their own gain. The criollos esp. early in Mexico and later in other regions drew on this to formulate an early form of patriotism. The Spanish, instead of favouring the overseas climates, would rather usually complain about and even use it to denigrate American groups.

On those last points I'd recommend "How to Write the History of the New World Histories, Epistemologies, and Identities in the Eighteenth-Century Atlantic World" by Jorge Cañizares-Esguerra on some of those later debates I mention (the 1st ch. deals with the 16/17th cs. also)