В такую погоду лучше остаться дома.

Because the phrase в такую погоду uses the accusative case.

• погода is feminine singular.
• Its accusative singular form is погоду.
• The adjective такая must agree with it, so it becomes такую.

So:

• nominative: такая погода = such weather
• accusative: в такую погоду = in such weather / in weather like this

This is a very common Russian pattern for talking about conditions or circumstances.

Good question. В can take different cases depending on meaning.

Usually:

• в + accusative = motion into something
• в + prepositional = location inside something

But in expressions like в такую погоду, в этот момент, в тот день, Russian often uses в + accusative to mean in/under such circumstances, at that time, or on that day.

So here в такую погоду is an established way to say in this kind of weather or in weather like this.

Here лучше means it is better or better to.

The sentence is an impersonal construction, so Russian does not need a subject like it:

• Лучше остаться дома. = It is better to stay home.
• В такую погоду лучше остаться дома. = In weather like this, it is better to stay home.

So лучше is not modifying a noun here. It is being used as a predicate meaning better in a general sense.

Because остаться is perfective, and it fits the idea of a single recommended action.

• остаться = to stay / remain, with focus on the result or one complete decision
• оставаться = to stay / remain, with focus on process, repetition, or general/habitual action

In this sentence, the speaker means something like:

• Given this weather, the better choice is to stay home.

That is why остаться sounds natural.

Compare:

• В такую погоду лучше остаться дома.
  = In weather like this, it’s better to stay home (this time / in this situation).

• В такую погоду лучше оставаться дома.
  = In weather like this, it’s better to stay home (generally / as a rule).

Both are possible, but the nuance is different.

Because дома means at home, while в доме means in the house/building.

This is an important distinction:

• дома = at home
• в доме = inside the house / in the building

So:

• остаться дома = stay home
• остаться в доме = stay in the house

In your sentence, the natural meaning is stay home, so дома is the right choice.

Yes, in a way. Russian often uses impersonal sentences where English would use it or a general you.

So:

• В такую погоду лучше остаться дома.

literally feels like:

• In such weather, better to stay home.

Natural English translations include:

• In weather like this, it’s better to stay home.
• You’d better stay home in weather like this.
• In this kind of weather, it’s best to stay home.

Russian does not need to say who exactly should stay home. It is understood generally.

Yes. Russian word order is flexible.

You could also say:

• Лучше остаться дома в такую погоду.
• Остаться дома в такую погоду лучше.

But В такую погоду лучше остаться дома sounds very natural because it starts with the situation first:

• in this kind of weather

Then it gives the recommendation:

• it’s better to stay home

So the original order is a very normal, smooth way to say it.

It most directly means such.

• такой / такая / такое / такие = such, this kind of

So в такую погоду is literally:

• in such weather
• more naturally: in weather like this

Depending on context, English may translate it as:

• in this weather
• in weather like this
• in such weather

All are possible, but the Russian word itself is closer to such / this kind of.

No. It sounds more like advice or a recommendation than a direct command.

• лучше остаться дома = it would be better to stay home

This is softer than:

• нужно остаться дома = it is necessary to stay home
• надо остаться дома = you need to stay home
• останься дома = stay home! (direct command to one person)

So лучше gives a more polite, less forceful tone.

Yes, that is often a very natural translation.

Possible English versions:

• In weather like this, it’s better to stay home.
• You’d better stay home in weather like this.
• It’s best to stay home in this kind of weather.

Just remember that the Russian sentence itself is impersonal, so it does not explicitly say you. English often adds you because it sounds natural.

In modern Russian, дома in this meaning is best learned as an adverb meaning at home.

Historically, it comes from an old case form of дом, but for learners it is most useful to treat it as a fixed word:

• Я дома. = I’m at home.
• Остаться дома. = Stay home.

So you do not usually analyze it the same way as a normal noun phrase like в доме.

Yes, absolutely. It sounds natural and idiomatic.

It is a normal way to give practical advice about bad weather, for example if it is:

• raining heavily
• snowing
• storming
• extremely cold

A Russian speaker might say this to mean that going out is probably not a good idea.