Без отопления в комнате холодно.

Russian often uses impersonal sentences with words like холодно, жарко, темно, скучно to describe a state. In the present tense, Russian normally omits “to be”:

• В комнате холодно. = It’s cold in the room. You can add быть in other tenses:
• Без отопления в комнате было холодно. (was cold)
• Без отопления в комнате будет холодно. (will be cold)

In this use, холодно is a predicative word (often called a “category of state” word). It behaves like the main predicate of an impersonal sentence:

• холодно = it is cold / it feels cold (in some place) It looks like an adverb, but grammatically it functions as the sentence’s main “state predicate.”

The preposition без requires the genitive case (Genitive = “of / without”):

• отопление (nominative)
• без отопления (genitive) So без + Genitive is the rule.

отопление usually means heating as a system/service (the heating in a building, central heating), not just “warmth” in general.

• без отопления = without heating (without the heating on / without a heating system)
  If you meant “without warmth,” you’d say something different (e.g., using тепло in other constructions).

After в meaning “in” (location, not motion), Russian uses the prepositional case:

• комната → в комнате This answers “where?” (где?) not “to where?” (куда?).
  Compare:
• в комнате (in the room, location)
• в комнату (into the room, motion → accusative)

No. There is no grammatical subject here. This is an impersonal structure:

• [In the room] [it is cold]. в комнате is a prepositional phrase of location (where it’s cold), not a subject.

Yes, word order is flexible. Putting без отопления first makes it the topic/condition (it emphasizes the cause/condition). Common variants:

• Без отопления в комнате холодно. (emphasis: without heating)
• В комнате без отопления холодно. (emphasis: in a room that has no heating)
• В комнате холодно без отопления. (emphasis at the end: it’s cold without heating)

It can mean either, depending on context:

• If you’re talking about a building where heating exists but isn’t working/turned on, без отопления = with no heating (currently).
• If describing a place that lacks a heating system, it can also mean a room without heating. If you want to be explicit about “turned off,” you might say something like без включённого отопления or just use context.

A natural way is:

• В комнате без отопления холодно. Here без отопления more directly describes комната (a room that has no heating).

Common conversational upgrades include:

• Без отопления в комнате очень холодно. (very cold)
• Без отопления в комнате просто холодина. (colloquial: really cold)
• Без отопления в комнате невозможно находиться. (It’s impossible to stay in the room without heating.)

Negation:

• Без отопления в комнате не холодно. (it’s not cold in the room without heating) — less common, but grammatically fine.

Conditional / hypothetical:

• Без отопления в комнате было бы холодно. (it would be cold…) Time-specific:
• Без отопления в комнате было холодно всю ночь. (was cold all night)