Если Вам холодно, лучше бы Вы взяли с собой термос и тёплые варежки.

They are capitalized because the speaker is addressing someone politely and formally, like you in a respectful singular sense.

In modern Russian, this capitalization is common in letters, messages, and other direct written communication when showing politeness. In many ordinary texts, you may also see вам and вы in lowercase even when the meaning is still formal.

Russian usually expresses physical or emotional states with an impersonal pattern:

[person in the dative] + [state word]

So:

Вам холодно = You are cold / You feel cold

Here, холодно is not an adjective agreeing with Вы. It is a state word meaning cold in the sense of how someone feels. That is why the person appears in the dative case: вам.

By contrast, Вы холодны would mean something more like you are cold/distant in personality or manner, not physically cold.

In the present tense, Russian normally does not use a word for am / is / are.

So:

Вам холодно
literally looks like To you cold, but it means You are cold or You feel cold.

This is completely normal in Russian. The present-tense to be is usually omitted.

Лучше бы means something like:

• it would be better if
• you’d better
• sometimes, depending on context, you should have

In this sentence, it gives advice in a somewhat soft, indirect way:

Лучше бы Вы взяли... = It would be better if you took...

It is less direct than a command, and it can sound thoughtful or slightly corrective.

Because Russian forms the conditional/subjunctive with:

past-tense form + бы

So взяли бы does not literally mean took in the past here. It means something hypothetical:

• would take
• should take
• it would be better if you took

This is a very important pattern in Russian:

• Я бы пошёл = I would go
• Вы бы сказали = You would say
• Лучше бы Вы взяли = It would be better if you took

So the past form is part of the grammar of unreality or suggestion, not necessarily real past time.

Because взять is perfective, and here the speaker means one complete action: take a thermos and warm mittens with you.

Perfective is natural when talking about a single practical action that should be done.
Брать is imperfective and would suggest an ongoing, repeated, or less bounded action, which does not fit as well here.

So:

• взять = to take, as one complete act
• брать = to take, be taking, take repeatedly, or in a more process-oriented sense

С собой means with you or along with you.

The expression взять с собой is very common and means to take something with you:

• взять с собой паспорт = take your passport with you
• взять с собой воду = take water with you

Without с собой, взять термос just means take a thermos, but it does not specifically emphasize bringing it along.

They are in the accusative case because they are the direct objects of взяли.

However, their forms happen to look like the nominative:

• термос is masculine singular inanimate, and for inanimate masculine nouns, accusative = nominative
• тёплые варежки is plural inanimate, and for inanimate plural nouns, accusative = nominative

So the forms do not visibly change here, even though the case is accusative.

Если Вам холодно means If you are cold or If you feel cold right now.

Если Вам будет холодно means If you get cold or If you are cold later / in the future.

So the sentence as written sounds like advice connected to a present situation. If the speaker were talking about some future outing, Если вам будет холодно... might be more natural.

Yes, in some contexts лучше бы + past form can sound like mild regret or criticism about something that was not done:

Лучше бы Вы взяли термос = You should have taken a thermos

But it can also mean a softer recommendation: It would be better if you took a thermos. The exact feeling depends on context and tone.

So this pattern often sits somewhere between:

• advice
• wish
• regret
• mild reproach

Yes. That version is more neutral and straightforward:

Лучше взять с собой термос и тёплые варежки = It’s better to take a thermos and warm mittens with you

Compared with that, лучше бы Вы взяли feels more personal and directed at the listener. It can sound softer, but also sometimes more pointed, depending on context.

Варежки are mittens.
Перчатки are gloves.

Since mittens are warmer, тёплые варежки fits well in a sentence about being cold.