Vyrazíme v pohorkách a vezmeme si pláštěnku, protože předpověď je špatná.

Because vyrazit is a perfective verb. In Czech, the present forms of perfective verbs usually refer to the future.

So:

• vyrazíme = we will set out / we’ll head out
• not we are setting out in a present-progressive sense

The same thing happens with vezmeme later in the sentence: it is also a perfective present form with future meaning.

Vyrazit often means to set out, to head off, to leave, or to start off on a trip or outing.

In this sentence, Vyrazíme is more natural than a plain půjdeme if the idea is we’ll head out / set off. It gives a slight sense of starting the outing, not just the basic act of going.

Pohorky are hiking boots.

The base form is pohorky (plural), and after the preposition v, Czech uses the locative case here:

• pohorky → basic plural form
• v pohorkách = in hiking boots

So pohorkách is the locative plural form.

Yes, literally it is in hiking boots, but idiomatically it means wearing hiking boots.

Czech often uses v with clothing and things worn on the body:

• v kabátě = wearing a coat
• v šatech = wearing a dress
• v pohorkách = wearing hiking boots

So it does not sound strange in Czech. It is just the normal way to say what someone is dressed in or equipped with.

Because s pohorkami would usually suggest with the boots in the sense of accompanying or carrying them, not necessarily wearing them.

Compare:

• v pohorkách = wearing hiking boots
• s pohorkami = with the hiking boots

In this sentence, the idea is clearly that we are going out wearing them, so v pohorkách is the right choice.

The little word si is the dative reflexive pronoun, and here it often means something like for ourselves / along with us.

So:

• vezmeme si pláštěnku = we’ll take a raincoat along / we’ll bring ourselves a raincoat
• vezmeme pláštěnku = we’ll take the raincoat

With clothes, food, drink, and personal items, vzít si is very common and natural. It often sounds more personal and more idiomatic than just vzít by itself.

Because vzít is perfective, and it fits a single completed action: we’ll take a raincoat.

• vezmeme si pláštěnku = we’ll take a raincoat
• bereme si pláštěnku would sound more like we are taking a raincoat or we usually take a raincoat, depending on context

In a sentence about a planned outing, Czech very naturally uses the perfective verb to express the future action.

Because pláštěnka is the direct object of vezmeme si, so it must be in the accusative singular.

Pláštěnka is a feminine noun of the -a type:

• nominative: pláštěnka
• accusative: pláštěnku

That is why the ending changes.

Pláštěnka means a raincoat or sometimes a rain poncho, depending on context.

It is something lightweight you take because of rain. In this sentence, the exact English translation could vary a bit, but the basic idea is clear: something waterproof to wear because the forecast is bad.

Because špatná is an adjective, and here it describes the noun předpověď.

• předpověď = forecast
• špatná = bad

So the structure is noun + být + adjective:

• Předpověď je špatná. = The forecast is bad.

Špatně is an adverb, so it would be used to describe a verb, not a noun.

Also, předpověď is feminine, so the adjective must agree with it:

• masculine: špatný
• feminine: špatná
• neuter: špatné

Yes, that is the natural interpretation.

By itself, předpověď can mean forecast or prediction more generally, but in this sentence the context makes weather forecast the obvious meaning:

• hiking boots
• a raincoat
• bad forecast

So Czech does not need to say předpověď počasí explicitly here.

The word order is not completely fixed. Czech word order is fairly flexible, and speakers often move things around for emphasis or style.

This version is very natural:

• Vyrazíme v pohorkách a vezmeme si pláštěnku, protože předpověď je špatná.

But you could also say:

• Protože je předpověď špatná, vyrazíme v pohorkách a vezmeme si pláštěnku.

The meaning stays basically the same. The difference is mostly about emphasis and information flow. The original sentence sounds like a neutral, natural statement.