Hieme frigus in terra manet, sed aestate calor redit.

Because they are in the ablative singular.

Here they express time when something happens:

• hieme = in winter
• aestate = in summer

In Latin, words for time are often put in the ablative without a preposition. So Latin says:

• hieme rather than in hieme
• aestate rather than in aestate

This is a very common pattern with words like days, seasons, and times.

Latin has no articles. It does not have separate words for a, an, or the.

So:

• frigus can mean cold or the cold
• calor can mean heat or the heat
• terra can mean earth, land, ground, or the earth

You figure out the best English wording from the context.

They are both nominative singular, because they are the subjects of their verbs.

• frigus ... manet = the cold remains
• calor redit = the heat returns

Even though the two nouns belong to different gender classes, they are both doing the action, so they are in the nominative.

Because these are two different uses.

• hieme / aestate use the ablative of time when: in winter, in summer
• in terra uses in + ablative to show location: in/on the earth, in the land, on the ground

So:

• time when something happens can often be expressed by the ablative alone
• place where something is often uses in with the ablative

Because in takes the ablative when it means in or on and shows location.

So:

• in terra = in/on the earth
• if there were motion into a place, Latin would usually use in with the accusative instead

A common contrast is:

• in terra = on the earth / in the land
• in terram = into the earth / onto the land

They are both third-person singular present active indicative verbs.

• manet = he/she/it remains
• redit = he/she/it returns

Here the subjects are singular nouns:

• frigus is singular, so manet is singular
• calor is singular, so redit is singular

The present tense here can be understood as a general truth: this is what happens in winter and summer.

Because each clause has one singular subject:

• frigus → singular subject → manet
• calor → singular subject → redit

Latin verbs must agree with their subject in number and person, just as in English:

• the cold remains
• the heat returns

Sed means but.

It is a coordinating conjunction joining two balanced clauses:

• Hieme frigus in terra manet
• sed aestate calor redit

It marks a contrast between winter and summer.

Yes. Latin word order is more flexible than English word order because the endings show the grammar.

This sentence begins with the time words:

• Hieme ...
• aestate ...

That helps emphasize the contrast between the two seasons.

A Latin writer could rearrange the words and still keep the basic meaning, for example:

• Frigus hieme in terra manet, sed calor aestate redit.

But the given order is neat and natural because it sets up the seasonal contrast first.

Frigus is a third-declension neuter noun.

Its nominative singular is frigus, and its genitive singular is frigoris. That genitive shows the stem frigor-.

So if you saw forms like frigore, frigoris, or frigori, they would all belong to the same noun.

Calor is a third-declension masculine noun.

Its dictionary form is:

• calor, caloris = heat

Like frigus, it belongs to the third declension, but unlike frigus, it is masculine, not neuter.

Because redit comes from redeo, which literally means go back or come back, and in good English that is often best translated as return.

So:

• calor redit = the heat returns

That is a natural English translation, even though the Latin verb is built from the idea of going back.

It can mean any of those, depending on context.

Common meanings of terra include:

• earth
• land
• ground

In this sentence, in terra probably means something like in the earth or on the earth / in the land, depending on the translation you were given. Latin often leaves this kind of nuance to context.