Pater caligas novas filio dat et dicit gelu in via magnum esse.

Because novas has to agree with caligas.

• caligas is accusative plural feminine
• so the adjective describing it must also be accusative plural feminine
• the accusative plural feminine form of novus, -a, -um is novas

So caligas novas means new boots as a direct object.

Filio is dative singular.

It is the person to whom the father gives something:

• Pater = the subject, the one doing the action
• caligas novas = the thing being given
• filio = the recipient, so it goes in the dative

This is very common with do / dare and dat:

• someone gives something
• to someone

So filio dat = he gives to the son / to his son.

Because Latin often shows that idea through the case ending, not through a separate word.

In English we say:

• to the son

In Latin the ending -o in filio already tells you that it is dative, so the meaning to/for the son is built into the form itself.

Latin word order is much freer than English word order because case endings show the job of each word.

So Latin can say:

• Pater caligas novas filio dat
• and still clearly mean that the father is the giver, the boots are what is given, and the son is the recipient

A very literal English-style order might be:

• Pater filio caligas novas dat

But Latin often puts the verb later, and it can move words around for emphasis or style.

Because after verbs like dicit Latin usually uses an indirect statement construction.

Instead of saying:

• He says that the frost is great

Latin says something more like:

• He says the frost to be great

That is why you get:

• dicit
  • subject of the statement + infinitive
• here: dicit gelu in via magnum esse

So esse is the infinitive to be, used because this is reported speech or reported thought.

There usually is no separate word for that in this kind of sentence.

English says:

• he says that ...

Latin normally just uses the accusative-and-infinitive construction after verbs of saying, thinking, knowing, hearing, and so on.

So:

• dicit gelu in via magnum esse

already means:

• he says that the frost on the road is great

The idea of that is understood from the structure.

Excellent question. In an indirect statement, the subject of the infinitive is normally in the accusative. So here gelu is functioning as an accusative subject of esse.

The reason it does not look different is that gelu is a neuter noun, and for this noun the nominative and accusative singular have the same form: gelu.

So even though the form looks unchanged, its job in the sentence is the one you would expect in indirect statement: the subject of esse.

Magnum agrees with gelu.

Since gelu is neuter singular, the adjective describing it must also be neuter singular:

• gelu ... magnum

And because this is in indirect statement, the adjective is part of the infinitive phrase:

• gelu ... magnum esse = the frost to be great / severe

So magnum is not random; it matches gelu in gender, number, and case.

Because in can take either the ablative or the accusative, depending on the meaning.

• in + ablative = in / on a place, showing location
• in + accusative = into / onto a place, showing motion toward

Here the meaning is location:

• on the road
• so Latin uses in via

If it meant movement onto the road, you would expect in viam.

Latin has no articles like English the or a.

So pater by itself could be understood as:

• the father
• a father
• or sometimes simply father

You decide from context and from the English meaning being aimed for. In this sentence, English usually makes it the father or father depending on the context of the story.

Latin often leaves out possessive words when they are obvious from the context.

Here, if the father is giving boots to the son, English may naturally say his son, but Latin does not need to spell that out unless there is a reason to emphasize it or avoid ambiguity.

So filio can naturally be understood as to his son if the context makes that clear.

There are three verbal forms:

• dat = he gives
• dicit = he says
• esse = to be

But only dat and dicit are finite verbs with person and number.
Esse is an infinitive, used inside the indirect statement after dicit.

Et joins the two main actions of the subject:

• Pater ... dat
• et dicit ...

So the father does two things:

1. he gives new boots to the son
2. he says that the frost on the road is severe

The same subject, pater, applies to both verbs.

It can have a range of related meanings, depending on context, such as:

• frost
• cold
• icy weather
• sometimes the idea of freezing conditions

So in this sentence the exact English wording may vary a little, but the grammar stays the same. The important point is that gelu is the thing that is said to be magnum.