Хотя ночью было холодно, у костра нам было тепло.

Yes. Хотя means although / even though.

So:

• Хотя ночью было холодно = Although it was cold at night
• у костра нам было тепло = we were warm by the campfire

It introduces a contrast: the night was cold in general, but near the fire, the speakers felt warm.

Ночью is the instrumental singular of ночь (night), and in Russian the instrumental is often used in expressions of time meaning during a certain part of the day or year.

So:

• утром = in the morning
• днём = in the daytime
• вечером = in the evening
• ночью = at night

This is a very common pattern, and it is best learned as a set expression.

Because холодно and тепло here are not regular adjectives describing a noun. They are predicative words used in impersonal sentences to describe a state or condition.

Russian often expresses feelings, weather, and general conditions this way:

• Было холодно. = It was cold.
• Было тепло. = It was warm.
• Мне было грустно. = I was sad.
• Нам было весело. = We were having fun.

There is no real subject like English it. Russian simply states the condition.

If you used холодный or тёплый, you would usually need a noun:

• холодная ночь = a cold night
• тёплый костёр would not make much sense in this context

So in this sentence, the speaker is talking about how the situation felt, not describing an object.

Because these are impersonal constructions.

In English we say it was cold, where it is a dummy subject. Russian usually does not use a dummy subject here. Instead, it uses a neuter singular past form:

• было холодно
• было тепло

This было does not agree with a visible subject, because there really is no normal subject in the sentence.

That is why you do not say были холодно or была холодно here.

У костра means by the campfire / near the campfire.

The preposition у usually means by, beside, near, at the place of and it takes the genitive case.

• костёр = campfire
• у костра = by the campfire

This is natural because the meaning is proximity, not being inside or on something.

Compare:

• у дома = by the house
• у окна = by the window
• у реки = by the river

So у костра is the normal way to say near the campfire.

Because the preposition у requires the genitive case.

The dictionary form is:

• костёр = campfire

But after у, it changes:

• у костра = by the campfire

This is a standard case change:

• дом → у дома
• лес → у леса
• костёр → у костра

So костра is genitive singular.

Because Russian often uses the dative to show the person who experiences a state.

• нам было тепло literally means something like to us it was warm
• natural English: we were warm

This pattern is extremely common:

• мне холодно = I am cold
• ему скучно = he is bored
• нам было хорошо = we felt good / we were comfortable

So нам is not the subject in the English sense. It marks the experiencer.

Yes, that is a useful literal way to understand it.

Russian very often expresses physical or emotional states like this:

• мне жарко = I am hot
• ей грустно = she is sad
• им было смешно = they found it funny / it was funny to them

So:

• нам = to us
• было тепло = it was warm

Literal structure: To us it was warm
Natural English: We were warm

In this sentence, repeating было is normal and clear, because each clause has its own predicate:

• Хотя ночью было холодно
• у костра нам было тепло

Each part expresses a separate state:

1. at night, it was cold
2. by the fire, we were warm

In some contexts Russian can omit repeated words if the meaning is obvious, but here keeping both было sounds natural and complete.

Both are possible, but the emphasis changes.

• У костра нам было тепло emphasizes by the campfire
• Нам было тепло у костра sounds a bit more like the main point is we were warm, with by the campfire added after

Russian word order is flexible, and speakers often place important or contrastive information earlier.

In this sentence, putting у костра first works well because it contrasts with the cold night in general:

• the night was cold,
• but by the campfire we were warm.

It can mean either, depending on context.

In this sentence, ночью было холодно most naturally means:

• it was cold at night
• or during the night it was cold

The exact English choice depends on style, but the Russian idea is simply that the coldness belongs to the nighttime period.

Yes, that is a very good natural translation.

Other natural versions are:

• Although the night was cold, we were warm by the campfire.
• Even though it was cold at night, we felt warm by the campfire.

The Russian does not force one single English wording. The important ideas are:

• nighttime cold
• warmth near the fire
• contrast introduced by Хотя

The correct spelling is тепло.

The letter ё is used only where it actually belongs, and this word does not contain ё. It comes from тёплый (warm), but the related predicative/adverb form is тепло.

So:

• тёплый = warm
• тепло = warmly / it is warm

This kind of vowel change is normal in Russian word formation.

No. The comma is needed here.

Хотя introduces a subordinate clause, and in Russian subordinate clauses are normally separated by a comma:

• Хотя ночью было холодно, у костра нам было тепло.

So the comma marks the boundary between:

1. Хотя ночью было холодно
2. у костра нам было тепло

Yes, около костра is possible and also means near the campfire.

But there is a slight difference in feel:

• у костра = by the campfire, right there beside it
• около костра = near the campfire, a bit more neutral or spatial

In this sentence, у костра sounds especially natural because it suggests being gathered right by the fire and feeling its warmth.

Yes, it is a very important and very common Russian pattern:

[dative experiencer] + было / будет / Ø + predicative word

Examples:

• Мне холодно. = I am cold.
• Ему было трудно. = It was hard for him.
• Нам будет весело. = We will have fun.
• Детям стало жарко. = The children became hot.

In your sentence:

• нам = experiencer in the dative
• было = past tense of to be
• тепло = state/condition

This pattern is one of the core ways Russian talks about physical sensations, emotions, and general states.