W lutym chodzę wcześniej spać, bo dni są jeszcze krótkie.

Because after w meaning in for a month, Polish uses the locative case.

• luty = February
• w lutym = in February

This is a very common pattern:

• w styczniu = in January
• w lutym = in February
• w marcu = in March

So w + month name usually requires the locative form.

Polish usually leaves out subject pronouns when they are clear from the verb ending.

• chodzę already means I go / I am going
• so ja chodzę is possible, but usually unnecessary

You would add ja only for emphasis, contrast, or clarity:

• Ja chodzę wcześniej spać, a on później. = I go to sleep earlier, and he later.

So in your sentence, no ja is needed.

Yes, chodzić can mean to walk, but it also has another very common use: to go regularly / habitually somewhere or to do something as a routine.

So:

• chodzę spać o dziesiątej = I go to bed / go to sleep at ten as a habit
• idę spać = I’m going to bed now / I’m off to sleep now

In this sentence, chodzę spać suggests a repeated pattern or routine in February, not a single one-time action.

This is an important distinction.

• chodzę spać = I go to bed / go to sleep regularly, as a habit
• idę spać = I’m going to bed now or I will go to bed now, a single occasion

Examples:

• W lutym chodzę wcześniej spać. = In February, I go to sleep earlier.
  → a general habit
• Jestem zmęczony, idę spać. = I’m tired, I’m going to bed.
  → right now

So chodzę is used because the sentence describes what the speaker generally does in February.

Wcześniej is an adverb, and here it means earlier.

It comes from:

• wcześnie = early
• wcześniej = earlier

Since it modifies the verb chodzę spać (how I go to sleep), Polish uses an adverb, not an adjective.

Compare:

• wcześniejsza godzina = an earlier hour
  → adjective, describing a noun
• chodzę wcześniej spać = I go to sleep earlier
  → adverb, describing the action

In this expression, chodzić spać / iść spać usually means to go to bed or to go to sleep.

So chodzę wcześniej spać is best understood as:

• I go to bed earlier
• or I go to sleep earlier

English can use either depending on context. Polish does not sharply separate those two ideas here.

Bo means because.

It is very common in everyday spoken and written Polish:

• chodzę wcześniej spać, bo dni są jeszcze krótkie
  = I go to sleep earlier because the days are still short

You could also use ponieważ, which also means because, but it sounds a bit more formal or neutral:

• W lutym chodzę wcześniej spać, ponieważ dni są jeszcze krótkie.

Both are correct. Bo is just more conversational and very common.

In Polish, a comma is normally used before bo.

So:

• ..., bo ...

This is standard punctuation, just as in many English sentences with because clauses, though Polish comma rules are generally stricter.

Here jeszcze means still.

So:

• dni są jeszcze krótkie = the days are still short

It shows that the situation continues. February is later than the deepest part of winter, but the days have not become long yet.

Be careful, because jeszcze can also mean yet, more, or another depending on context.

Examples:

• Jeszcze nie śpię. = I’m not asleep yet.
• Poproszę jeszcze herbatę. = I’d like some more tea.
• jeszcze jeden dzień = one more day

Because dni is the plural form of dzień.

• dzień = day
• dni = days

Since the subject is plural, the verb must also be plural:

• dzień jest krótki = the day is short
• dni są krótkie = the days are short

So są is the plural form of to be.

Because dni is the subject of the sentence, so the adjective must be in the nominative plural to match it.

• dni is plural
• dzień is a masculine non-personal noun
• adjectives with masculine non-personal plural subjects usually end in -e in the nominative

So:

• krótkie dni = short days
• dni są krótkie = the days are short

Compare:

• wysocy mężczyźni = tall men
  → masculine personal plural, so -i
• krótkie dni = short days
  → non-masculine-personal plural, so -e

krótkich would be a different case, such as genitive or locative in some contexts, so it would not fit here.

That is normal in Polish when using to be plus an adjective:

• Dom jest duży. = The house is big.
• Dni są krótkie. = The days are short.

You could also put the adjective before the noun in a noun phrase:

• krótkie dni = short days

But in this sentence, the structure is not a noun phrase. It is:

• dni = subject
• są = verb
• krótkie = predicate adjective

So dni są krótkie is exactly what you would expect.

Polish word order is fairly flexible, but some versions sound more natural than others.

The original sentence:

• W lutym chodzę wcześniej spać, bo dni są jeszcze krótkie.

is very natural. It starts with the time phrase W lutym, then gives the main action, then the reason.

You could rearrange parts for emphasis:

• Chodzę wcześniej spać w lutym, bo dni są jeszcze krótkie.
  Also possible, but a bit less neutral.
• Bo dni są jeszcze krótkie, w lutym chodzę wcześniej spać.
  Grammatically possible, but more marked.

So the original order is probably the best default choice for a learner.

Usually it means in February, but in practice that often overlaps with during February.

In this sentence, w lutym suggests a general habit or pattern within that month:

• In February, I go to sleep earlier

So in English, either in February or during February could fit depending on style, but in February is the most direct match.

Yes, but it is a little different.

• chodzę wcześniej spać = I go to bed earlier / I go to sleep earlier, as a habit
• kładę się wcześniej spać = I lie down / go to bed earlier

kłaść się focuses more on the act of lying down or going to bed physically.
chodzić spać is a very common idiomatic way to talk about one’s sleeping schedule or bedtime routine.

So your original sentence sounds very natural.