Il se peut qu’il fasse froid en hiver, mais le radiateur de la chambre semble neuf.

Il se peut que is a fixed expression meaning it may be that, it is possible that, or perhaps.

So:

• Il se peut qu’il fasse froid en hiver
  = It may be cold in winter

A few important points:

• The il here does not refer to a person or thing. It is an impersonal il, like it in it is raining.
• se peut comes from se pouvoir, but in modern French you mostly learn it as the expression il se peut que rather than as a normal verb you freely build in many ways.
• This expression is commonly followed by the subjunctive, which is why you get qu’il fasse and not qu’il fait.

It is a slightly more formal or written-sounding way to express possibility than simply saying peut-être.

Because il se peut que requires the subjunctive mood.

• faire in the present subjunctive for il is fasse
• the ordinary present indicative form would be fait

So:

• qu’il fasse froid = that it may be cold
• il fait froid = it is cold

French often uses the subjunctive after expressions involving:

• possibility
• doubt
• emotion
• necessity
• judgment

Since il se peut que expresses possibility, the subjunctive is used.

A useful comparison:

• Je pense qu’il fait froid. → indicative, because this is presented as a statement/opinion
• Il se peut qu’il fasse froid. → subjunctive, because this is only a possibility

In French, many weather expressions use faire, where English uses to be.

So:

• Il fait froid = It is cold
• Il fait chaud = It is hot
• Il fait beau = The weather is nice
• Il fait mauvais = The weather is bad

That is why in the sentence you see:

• qu’il fasse froid

Literally, this is something like that it do cold, but you should not translate it word-for-word. Just learn faire + weather expression as the normal French pattern.

Because froid here is used as part of the fixed weather expression faire froid.

In this structure:

• faire froid = to be cold
• faire chaud = to be hot

No article is used.

Compare:

• Il fait froid. = It is cold.
• J’ai froid. = I am cold.

In the first sentence, froid describes the weather.
In the second, it describes how a person feels.

So froid here behaves more like part of an expression than like a noun needing an article.

French normally uses en with seasons when speaking generally:

• en hiver = in winter
• en été = in summer
• en automne = in autumn
• au printemps = in spring

Printemps is the exception: it takes au, not en.

So en hiver is the normal way to say in winter in a general sense.

You may also see l’hiver in some contexts:

• L’hiver, il fait froid. = In winter, it’s cold.

But in your sentence, en hiver is the straightforward and natural choice.

Because of elision.

When que comes before a word starting with a vowel sound, the final e drops:

• que il → qu’il
• que elle → qu’elle
• si il does not become s’il by the same rule? Actually yes: si il → s’il

This is very common in French and helps pronunciation flow more smoothly.

So:

• Il se peut qu’il fasse froid
  not
• Il se peut que il fasse froid

Yes, mais simply means but.

It connects two ideas:

• Il se peut qu’il fasse froid en hiver
• mais le radiateur de la chambre semble neuf

So the sentence is contrasting:

• the possibility that it may be cold in winter with
• the fact that the bedroom radiator seems new

The exact logical relationship depends on context, but grammatically mais is just the normal coordinating conjunction but.

French often uses de where English uses a noun-as-adjective structure.

English can stack nouns:

• bedroom radiator
• kitchen door
• school bus

French usually prefers:

• le radiateur de la chambre = the radiator of the bedroom / the bedroom radiator
• la porte de la cuisine = the kitchen door
• le bus de l’école or other rephrasing depending on meaning

So de la chambre identifies which radiator we mean: the one belonging to or located in the bedroom.

This is one of the most common structural differences between English and French noun phrases.

Because chambre is a feminine singular noun.

The preposition de combines with definite articles like this:

• de + le = du
• de + les = des
• de + la = de la
• de + l’ = de l’

Since chambre is feminine and singular:

• la chambre
• therefore de la chambre

Examples:

• le toit du garage = the roof of the garage
• la fenêtre de la chambre = the window of the bedroom
• la porte de l’hôtel = the door of the hotel

Because neuf is the adjective meaning new, and it must agree with the noun it describes.

Here the noun is:

• le radiateur — masculine singular

So the adjective is also masculine singular:

• neuf

Forms of neuf:

• masculine singular: neuf
• feminine singular: neuve
• masculine plural: neufs
• feminine plural: neuves

Examples:

• Le radiateur semble neuf.
• La machine semble neuve.
• Les radiateurs semblent neufs.

Also, nouvel is not the same thing as the regular predicate form used here. It is a special form of nouveau used before a masculine singular noun beginning with a vowel sound:

• un nouvel appartement
• un nouveau radiateur

But after sembler, you normally use the adjective directly as a predicate:

• Le radiateur semble neuf.

Because sembler means to seem or to appear, while être means to be.

So there is an important difference:

• Le radiateur est neuf. = The radiator is new.
• Le radiateur semble neuf. = The radiator seems new.

With semble neuf, the speaker is not stating the radiator is definitely new, only that it appears new.

This matches the cautious or observational tone of the sentence.

It usually means new, but it can also mean nine.

French has two different words spelled the same way:

• neuf = new
• neuf = nine

Context tells you which one it is.

In your sentence:

• le radiateur ... semble neuf

it clearly means new, because after sembler we expect an adjective describing appearance.

You can also hear a pronunciation difference sometimes:

• adjective neuf can have a final f sound in many contexts
• number neuf is also pronounced with the f sound when said alone

But for a learner, the main thing is: in this sentence it definitely means new.

Yes. A natural English rendering could be:

• It may get cold in winter, but the bedroom radiator seems new.
• It may be cold in winter, but the radiator in the bedroom seems new.

Both are good depending on context.

A very literal version would be:

• It may be that it is cold in winter, but the radiator of the room seems new.

That is grammatical English, but less natural. When translating from French, it is usually better to keep the meaning and tone rather than copy every structure exactly.