Mater puellae pallium imponit, quia ventus frigidus est.

Because imponere often takes:

• an accusative for the thing being placed
• a dative for the person or thing on whom / on which it is placed

So in Mater puellae pallium imponit:

• pallium = the cloak → accusative
• puellae = to/on the girl → dative

A very literal sense is The mother places a cloak onto the girl, though natural English would be The mother puts a cloak on the girl.

Yes, puellae can be either:

• genitive singular = of the girl
• dative singular = to/for the girl

The form is ambiguous by itself. But the verb tells you which meaning makes sense here. Since imponit commonly takes a dative of the person receiving the thing, puellae is understood as to/on the girl, not of the girl.

Because it is the direct object of imponit.

The mother is doing the action of putting, and the thing being put is the cloak, so pallium is accusative singular.

Mater is nominative singular, because it is the subject of imponit.

It means mother and belongs to the third declension. Its basic forms are:

• nominative: mater
• genitive: matris

So here mater is the one performing the action.

Latin word order is much more flexible than English word order because the endings show the grammatical roles.

Placing the verb at the end is very common in Latin, especially in straightforward prose. So:

• Mater puellae pallium imponit

is a normal Latin order.

But other orders could also be possible, for example:

• Mater pallium puellae imponit
• Pallium mater puellae imponit

The meaning stays basically the same, though the emphasis can shift.

Imponit is from imponere, which literally means something like to place on, to put on, or to set upon.

In this sentence, the most natural English translation is puts on:

• The mother puts a cloak on the girl

It is built from:

• in-/im- = on, onto
• ponere = to place, put

Classical Latin has no articles.

So a noun like mater can mean:

• mother
• the mother
• sometimes even a mother

You decide from context which English article is best. The same is true for:

• puellae = the girl / a girl / to the girl
• pallium = the cloak / a cloak
• ventus = the wind / a wind

That is a very normal Latin clause order:

• quia = because
• ventus = the wind
• frigidus = cold
• est = is

Latin often puts est at the end, and adjectives commonly come after the noun, so ventus frigidus est is perfectly standard.

Other orders could also occur, such as quia frigidus ventus est, but the given version is very natural.

Because it agrees with ventus, which is masculine singular nominative.

Latin adjectives must agree with the nouns they describe in:

• gender
• number
• case

So:

• ventus = masculine singular nominative
• frigidus = masculine singular nominative

If the noun were feminine, the adjective would change form. For example:

• aura frigida = the cold breeze

Because its subject is ventus, which is singular:

• ventus = the wind
• est = is

So ventus frigidus est means the wind is cold.

If the subject were plural, Latin would use a plural verb, for example:

• venti frigidi sunt = the winds are cold

Quia means because and introduces a clause giving the reason:

• Mater puellae pallium imponit = The mother puts a cloak on the girl
• quia ventus frigidus est = because the wind is cold

So the second clause explains why the mother is doing that.

Yes: in Latin, adjectives can come before or after the noun. Here the adjective comes after:

• ventus frigidus

This is very common and does not sound strange in Latin. English usually prefers cold wind, but Latin often uses either order depending on style and emphasis.

So you should not assume that Latin adjective order always matches English adjective order.

A very literal translation is:

• Mother places a cloak on the girl

A more natural English translation is:

• The mother puts a cloak on the girl

That is often the best approach with Latin: understand the grammar literally, but translate into natural English.

Here the key pattern is:

• subject: mater
• dative person: puellae
• accusative thing: pallium
• verb: imponit

So the sentence means that the mother is putting the cloak onto the girl, not that the girl owns the cloak.