Зимой кожа на руках становится сухой.

Yes. Зимой means in winter / during the winter.

A common thing that surprises English speakers is that Russian often uses the instrumental case without a preposition for seasons and parts of the day in an adverbial sense:

• зимой = in winter
• летом = in summer
• утром = in the morning
• вечером = in the evening

So Зимой кожа на руках становится сухой literally has the sense In winter, the skin on the hands becomes dry.

Russian commonly expresses this idea with кожа на руках = the skin on the hands.

Here:

• кожа = skin
• на руках = on the hands

This is a very natural Russian way to talk about where the skin is located. English often prefers the skin on your hands or hand skin, but Russian usually says кожа на руках.

You could also sometimes hear кожа рук = the skin of the hands, which is a bit more compact or formal-sounding. But кожа на руках is very common and natural in everyday speech.

Because на руках is describing location, not movement.

Compare:

• на руках = on the hands / on the hands as a location
• на руки = onto the hands / to the hands as direction or destination

In this sentence, the skin is not moving onto the hands. It is simply located there, so Russian uses:

• на + prepositional case
• руках = prepositional plural of руки

So кожа на руках means skin on the hands.

Because руки means hands, and the sentence is talking about the skin on the hands in general, usually both hands.

Russian often uses the plural here the same way English does:

• hands
• руки

So:

• на руках = on the hands

If you were talking about just one hand, it would be:

• на руке = on the hand

Because after the verb становиться / стать meaning to become, Russian normally uses the instrumental case for the noun or adjective that describes the new state.

So:

• кожа is feminine singular
• the instrumental feminine singular form of сухая is сухой

That is why we get:

• кожа становится сухой = the skin becomes dry

This is a very important pattern:

• Он стал врачом = He became a doctor
• Она стала счастливой = She became happy
• Кожа становится сухой = The skin becomes dry

If you said сухая, that would sound wrong in this structure.

The dictionary form is сухой, which is the masculine nominative singular form.

Adjectives change form depending on gender, number, case, and syntax. Here are a few forms of this adjective:

• сухой = masculine nominative
• сухая = feminine nominative
• сухое = neuter nominative
• сухие = plural nominative
• сухой = feminine instrumental

Since кожа is feminine, you might expect сухая, but because it comes after становится, Russian uses the instrumental, so the correct form is сухой.

Because Russian present tense here expresses a general repeated situation or what tends to happen.

So становится means something like:

• becomes
• gets
• tends to become

In context, the sentence means:

• In winter, the skin on the hands becomes dry
• or In winter, the skin on your hands gets dry

It is not necessarily describing one single moment happening right now. It can describe a general fact or habitual process.

Because the sentence is describing a change of state.

• кожа сухая = the skin is dry
• кожа становится сухой = the skin becomes dry / gets dry

So становится adds the idea that the skin was not dry before, or was less dry, and then it changes into that condition.

English often uses gets in exactly this kind of sentence, and Russian становится works similarly.

Yes, but the meaning shifts slightly.

• Кожа на руках становится сухой = the skin on the hands becomes dry
• Кожа на руках сохнет = the skin on the hands is drying out / dries out

Становится сухой focuses on the resulting state: it becomes dry.
Сохнет focuses more on the process of drying.

Both can be natural, but they are not exactly identical.

Because Russian often leaves out possessive words like my, your, or his/her when the meaning is general or obvious from context.

So кожа на руках can naturally mean:

• the skin on the hands
• the skin on your hands
• the skin on one’s hands

depending on context.

If Russian wants to be specific, it can add a possessive:

• кожа на моих руках = the skin on my hands
• кожа на твоих руках = the skin on your hands

But in a general statement like this, leaving it out sounds very natural.

The sentence as given is very natural:

• Зимой кожа на руках становится сухой.

But Russian word order is fairly flexible, and other versions are possible depending on emphasis. For example:

• Кожа на руках зимой становится сухой.
• Сухой зимой кожа на руках становится — grammatically possible, but unnatural in normal speech
• На руках кожа зимой становится сухой. — possible if you are emphasizing on the hands

The original order is the most neutral and standard: time first, then subject, then the rest.

Because Russian has no articles.

So кожа can mean:

• skin
• the skin

You understand which one is meant from context. In this sentence, English naturally uses the skin, but Russian simply says кожа.

That is completely normal.

Кожа is in the nominative singular.

It is the grammatical subject of the sentence:

• кожа = the skin

The verb agrees with it in singular:

• становится = becomes

So the basic structure is:

• Зимой = in winter
• кожа = the skin
• на руках = on the hands
• становится сухой = becomes dry

There is definitely a pattern, and it is worth learning.

Russian often uses the instrumental form of certain time words adverbially:

• зима → зимой = in winter
• весна → весной = in spring
• лето → летом = in summer
• осень → осенью = in autumn
• утро → утром = in the morning
• день → днём = in the daytime / during the day
• вечер → вечером = in the evening
• ночь → ночью = at night

So зимой is not random; it is part of a useful pattern.