It was well known in the ancient and medieval world that the seasons on the other side of the world would be the opposite of their own. This is a basic implication of their understanding of the composition of the world and the cause of the seasons.

The Greeks and Romans divided the world into 5 latitudinal bands or zones according to the suns impact on their climate. So, for example, in his didactic poem the Georgics, Vergil describes the composition of the world:

To this end the golden Sun rules his circuit, portioned out in fixed divisions, through the world’s twelve constellations. Five zones comprise the heavens; whereof one is ever glowing with the flashing sun, ever scorched by his flames. Round this, at the world’s ends, two stretch darling to right and left, set fast in ice and black storms. Between these and the idle zone, two by grace of the gods have been vouchsafed to feeble mortals; and a path is cut between the two, wherein the slanting array of the Signs may turn. (1.231-9)

This created a stratified image of the world, north to south, within which they understood their inhabited section of the world to comprise one half of the northern inhabitable zone. Resulting in an image of the world that looks like this (this is where we get the ideas of the tropics of cancer and capricorn as well as arctic and antartic circles, as in this diagram). We see this form depicted frequently in medieval maps, particularly those in copies of Macrobius's Commentary on the Dream of Scipio.

So we get a standard appraisal of the inhabitable areas of the world and their relationships as a standard feature of late antique handbooks, like Macrobius's aforementioned commentary. So, in Martianus Capella's (fl. c. 410-20) Marriage of Philology and Mercury (6.603-6) he explains that the earth is divided into two hemispheres, northern and southern, and that we live in the northern and the antipodes are believed to live in the southern. He explains that each hemisphere also has two inhabitable zones on opposite sides of the globe, like an eastern and western hemisphere (although ancient and medieval authors didn't call them this!), creating two more sets of antipodes, one for us and one for our southern antipodes. So there are in total 4 sets of distinct habitable areas, 2 on opposite sides of the north and two on opposite sides of the south (lets say N+ (us), N-, S+, S-. He then goes on to explain the relationship of these regions:

Our [ie. N+] condition is distinct from theirs [ie. S+] in the oppositeness of our seasons. When we are scorched with summer's heat, they are numbed with cold; when spring here bedecks the meadows with flowers, the heat of summer there is yielding to the gentle warmth of autumn; when we have our shortest day, they have their longest; we get a clear view of Arctos [the Bear], which is wholly invisible to them. Our antipodes (N-) experience with us a common period of winter and the heat of summer, but we have our days and nights at opposite times from them... (6.605-6)

This would have been readily available knowledge to anyone in the middle ages as it was described in the most common medieval encyclopedia, the Etymologies of Isidore of Seville (~560-636):

1. There are five zones (zona) in the heavens, and based on their differences, certain regions are inhabited due to their temperate climate, and certain regions are uninhabitable from the brutality of the cold or heat. They are called zones or ‘circles’ (circulus) because they consist of a circular band (circumductio) of the sphere. 2. The first of these circles is called ἀρκτικὸς (i.e. “arctic”), because the conspicuous constellations called Arctos (i.e. the Bears) are enclosed within it. The second circle is called θερινὸς τροπικὸς (i.e. “summer tropic”) because in this circle the sun makes it summer when it is at its northern limit, and it does not travel beyond this circle, but rather turns back at once. Whence it is called τροπικὸς (cf. trop , “turning”). 3. The third circle is called ἡμερινὸς, and is called ‘equinoctial’ (aequinoctialis) by Latin speakers, because the sun, when it goes across to this zone, makes the day and night equal length (aequinoctium) – for the term Ἡμερινὸς means ‘day and night’ in Latin.29 The central part of the sphere is seen to be made up of this band. The fourth circle is called ἀνταρκτικὸς (i.e. “antarctic”) because it is opposite to the circle that we call ἀρκτικὸν. 4. The fifth circle is called χειμερινὸς τροπικὸς (i.e. “winter tropic”). It is called ‘winter’ (hiemalis) or brumalis (i.e. another word for “winter”) by Latin speakers, because when the sun travels to this circle, it makes winter for those who are in the north, and summer for those who live in the southern regions. (3.44.1-4)

We can equally see this displayed visually in the middle ages. For example, in his encyclopaedia, the Liber Floridus (c.1120), Lambert of Saint-Omer includes a Macrobian style map of the the globe. (See here the one labelled "zonal world map" and here for a high def version which can only be viewed one page at a time.) On the left you can see the northern temperate zone with the a map of Europa, Africa and Asia in a fairly evident T diagram form. On the right is a depiction of the southern continent with a block of text on it. The text explains that we have never seen this land, nor is it accessible to Adams children. But, around the middle it explains that:

The philosophers says that the antipodes inhabit this [region]. Whom [the philosophers] assert are separated from us by a difference of seasons (temporum). For when we are scorched by summer, they are frozen by winter (frigore).