samui yoru wa, hayame ni futon ni hairimasu.

Because 寒い is an i-adjective, and i-adjectives can directly modify nouns.

So:

• 寒い夜 = a cold night / cold nights

This works like:

• 暑い日 = a hot day
• 新しい本 = a new book

There is no need for な or any particle here.

In 寒い夜は, the は marks cold nights as the topic.

So the sentence is setting up a condition or situation:

• As for cold nights, ...
• On cold nights, ...

This is very natural in Japanese when talking about what one usually does in a certain situation.

Both particles can relate to time, but they do different things.

• 寒い夜は = on cold nights / as for cold nights
  This sounds like a general habit or repeated action.
• 寒い夜に would point more to a specific time when something happens.

Since 入ります here sounds like a regular action or habit, は fits very well.

早め means a bit early, fairly early, or earlier than usual.

It comes from 早い (early) and has the nuance of:

• not necessarily extremely early
• just somewhat earlier than normal or expected

So 早めに means:

• a little early
• earlier than usual

The に makes 早め function adverbially, so it describes how the action is done.

• 早めに入ります = go/get in early

This is similar to other noun-like words that take に when used as adverbs.

Compare:

• 静かに話す = speak quietly
• 早めに寝る = go to bed a bit early

布団に入る literally means to get into the futon/bed.

It focuses on the act of getting into bed, while 寝る means to sleep / go to sleep.

So the nuance is slightly different:

• 寝ます = sleep / go to bed
• 布団に入ります = get into bed

In English, depending on context, both might be translated as go to bed, but Japanese is being a bit more physical and specific here.

Here, に marks the destination or place one enters.

With the verb 入る (to enter), the place entered is usually marked by に.

So:

• 布団に入る = enter/get into the futon
• 部屋に入る = enter the room
• お風呂に入る = get in the bath

This に is different from the に in 早めに.
They happen to look the same, but they serve different grammatical roles.

Because 入ります is the normal, simple polite form of 入る.

In this sentence, the speaker is just stating a habit:

• On cold nights, I get into bed early.

There is no need for extra nuance like movement away from the speaker, ongoing action, or directionality. So the plain polite form is the most natural choice.

Not exactly.

• 布団 = a Japanese-style futon, bedding laid out for sleeping
• ベッド = bed

In many translations, 布団に入る may be rendered as get into bed, because that is the natural English equivalent. But the actual Japanese word here is specifically 布団.

Japanese often omits the subject when it is obvious from context.

So this sentence could imply:

• I get into bed early on cold nights
• We get into bed early on cold nights
• or another understood subject

In many everyday Japanese sentences, the subject is left unsaid unless it needs emphasis or clarification.

It most naturally sounds like a habit or general tendency.

That comes from:

• 寒い夜は = on cold nights / whenever it’s a cold night
• 入ります in non-past polite form, which often expresses habitual action

So the feeling is:

• When the nights are cold, I tend to get into bed early.

Formally, 入ります is the non-past polite form.

In Japanese, the non-past can mean:

• present
• future
• habitual action

Here, it is best understood as habitual:

• (I) go/get into bed early on cold nights.

So even though English may use a simple present for habits, Japanese uses the non-past form for that too.