I can think of one example of a Spanish writer – though not an explorer – mentioning differences in climate regarding South America. José de Acosta was a Jesuit who spent 15 years traveling in South and Middle America (esp. Peru). Upon his return to Spain he wrote his Natural and Moral History of the Indies published in 1590, often described as very „advanced“ for its time in its description of natural phenomena (including geophysics) and containing elements of proto-ethnology.

Books II and III of the History focus on meteorological observations. An interesting part comes in the chapter titled „Of Aristotle’s Opinion of the New World and What It Was that Caused Him to Deny It“:

In addition to the reasons I have mentioned there was another that moved the ancients to believe that it was impossible for men to pass from there to this New World; and they said that in addition to the immensity of the Ocean the heat of the region that they call torrid, or burnt, was so extreme that it would not allow men—no matter how daring—to cross it either by land or sea, from one pole to the other. For even those philosophers who affirmed that the world was round, as indeed it is, and that there was habitable land near the two poles, denied in spite of this that human beings could live in the middle region that includes the two tropics, which is the greatest of the five zones or regions into which the cosmographers and astronomers divided the world. The reason they gave as to why this Torrid Zone was uninhabitable was the burning heat of the sun, which is always so close overhead and scorches that whole region and hence causes it to lack water and vegetation. Aristotle was of this opinion, and, though a great philosopher, he was mistaken in this...

Other disagreements with Aristotle include Acosta's analysis of the trade winds. Acosta also discussed the variety of climate in tropical regions which varied according to its location near the coast, or in the highlands. According to him, different climates are found in the same latitude because of the proximity of the ocean, the influence of rains and winds, and the properties of the land. So we don't get a clear description of the reversal of seasons yet, but still a disagreement with traditional authorities like Aristotle, who had described these regions as uninhabitable following European climate patterns. Acosta's views can be seen as adding new perspectives while still holding to the geocentric theory – seeing how Copernican views were not yet widely accepted at that point in time.

Anthony Pagden (in his European Encounters With the New World, p. 53-54) has a short further discussion on Acosta's views that I found interesting:

The Jesuit historian José de Acosta, for instance, tells us that on finding himself cold at midday yet with the tropical sun directly overhead - an impossible situation according to ancient meteorology - he 'laughed and made fun of Aristotle and his philosophy'. The difficulty, however, was always seeing the discrepancy between the observation and the text, particularly since no observation or experiment was ever conducted with the purpose of verifying (much less falsifying) the stamenents made in the text. When experience directly contradicted the text, it was the experience, which was unstable because of its novelty, which was likely to be denied or at least obscured. [...] Acosta may have laughed at Aristotle's meteorology, but he accepted all of his psychology, and most of his sociology and the anthropology to be found in the Politics and the Etics.

Summing up: I can't speak for earlier explorers' views of the seasons, but seeing as Acosta wrote a very well-received work on natural history in the late 16th c., I doubt that earlier Europeans lacking scholarly training would have held much more advanced views.
The example of José de Acosta has shown first that the new experiences of the Americas led him to differ from Aristotle's highly influential views on meteorology. He described weather phenomena in South America that would have been impossible according to Aristotle: Including the hospitabilty of the lands despite being so far south, and his feeling cold despite the sun shining overhead. He did not make a reversal of the seasons more explicit in his work. These new views however did not mean that all classical knowledge was discarded with. The canon of bible and classical authors (incl. the geocentric model) remained an important frame of reference during this time period. Nonetheless, authors like Acosta out of necessity (due to the "newness" of the "discoveries") initiated a trend of turning to their own voice rather than traditional authorities to confirm the authority of their writings for European audiences who were far from the Americas.

Sources:

• José de Acosta, Natural and Moral History of the Indies, transl. Frances López-Morillas, 2002.

• Anthony Pagden, European Encounters with the New World. From Renaissance to Romanticism, 1993.

Pigafetta's account of Magellan's circumnavigation (1519-1522) includes the observation that the duration of the days, like the seasons, were reversed; he attested, in partial proof, that there were only three hours of night (as in, no light at all, as opposed to late evening or early morning which we might consider "night" today) in late October. That he referred to these seasons correctly per the southern hemisphere--not "a winter without night" or anything like that--is telling. (See page 61 of this admittedly old translation for the passage in question; pages up to 49 also show the implication.) Details remain a bit sketchy, and you can't always trust Pigafetta, who veered towards the sensational quite a bit--but noting the point in itself is telling. As to whether they understood the reason for the reversal of seasons, it depends on whether you require that the understanding simply involve the sun exposure or a knowledge of the structure of the solar system as a whole (that is, heliocentricity); Pigafetta does not state that clearly. I'll have a look at Vasco da Gama's journals in translation when I'm back at my office and see if anything appears there relative to the Cape of Good Hope.