Я люблю ходить на лыжах зимой, когда в парке тихо.

After любить when you mean to like doing something, Russian normally uses an infinitive:

• Я люблю читать. = I like to read.
• Я люблю гулять. = I like walking.
• Я люблю ходить на лыжах. = I like skiing / going skiing.

So люблю is the main verb, and ходить tells you what activity the speaker likes.

This is a very common question because Russian has two verbs for to go on foot:

• идти = to be going right now, in one direction
• ходить = to go regularly, generally, or back and forth

Here the sentence is about a general habit or preference, not one specific trip. That is why Russian uses ходить:

• Я люблю ходить на лыжах зимой. = I like to ski in winter / I like going skiing in winter.

If you said Я люблю идти..., it would sound wrong here, because идти is for a concrete motion in progress, not for a repeated activity you enjoy in general.

Literally, ходить на лыжах means something like to go on skis.

Russian often describes activities this way:

• ходить на лыжах = to ski
• ездить на велосипеде = to ride a bicycle
• плавать = to swim

So instead of a single verb exactly matching English to ski, Russian very often uses this expression with на лыжах.

A related expression is кататься на лыжах, which also means to ski. The difference is often:

• ходить на лыжах emphasizes moving along on skis, often more like cross-country skiing
• кататься на лыжах is a broader, very common way to say skiing, often especially recreationally

In many everyday contexts, both can work, but ходить на лыжах is completely natural.

Because Russian uses a prepositional expression here: на лыжах = on skis.

The noun лыжи is in the plural because skis come as a pair, and after на in this expression it becomes prepositional plural:

• nominative: лыжи
• prepositional: на лыжах

This pattern is common in Russian for means of movement or equipment:

• на машине = by car / in a car
• на автобусе = by bus
• на лыжах = on skis

So ходить на лыжах is a fixed, natural expression.

Зимой is the instrumental form of зима, and in Russian the instrumental is often used to mean in the winter, during winter, or in winter.

This is a very common time expression:

• зимой = in winter
• летом = in summer
• осенью = in autumn
• весной = in spring

So:

• Я люблю ходить на лыжах зимой. = I like skiing in winter.

You can also say в зимнее время or other longer expressions, but зимой is the normal simple way.

Russian uses different prepositions depending on how a place is conceptualized.

• в usually means in or inside a space/area
• на often means on, but it is also used with certain places by convention

A park is normally treated as an enclosed or defined area, so Russian says:

• в парке = in the park

Compare:

• в городе = in the city
• в лесу = in the forest
• в школе = at school / in school

But:

• на стадионе = at the stadium
• на площади = in the square
• на улице = in the street / outside

So в парке is simply the normal choice with парк.

Because когда в парке тихо is a subordinate clause.

Russian punctuation requires a comma before a subordinate clause introduced by words like:

• когда = when
• если = if
• потому что = because
• что = that

So:

• Я люблю ходить на лыжах зимой, когда в парке тихо.

Literally, the structure is:

• main clause: Я люблю ходить на лыжах зимой
• subordinate clause: когда в парке тихо

The comma is required in standard Russian writing.

Because тихо here is not describing a noun directly. It means it is quiet.

In Russian, words like тихо, холодно, жарко, темно are often used in impersonal sentences:

• Здесь тихо. = It is quiet here.
• На улице холодно. = It is cold outside.
• В комнате темно. = It is dark in the room.

So когда в парке тихо literally means when it is quiet in the park.

If you used тихий, that would be an adjective modifying a noun:

• тихий парк = a quiet park

But here there is no noun being described; the sentence is describing the general atmosphere.

Yes, often it can be omitted in Russian if the subject is clear from the verb form.

• Люблю ходить на лыжах зимой, когда в парке тихо.

This still clearly means I like skiing in winter, when the park is quiet, because люблю is first person singular.

However, Я is perfectly natural too. Including it can:

• make the sentence a bit more explicit
• add slight emphasis
• sound more balanced in some contexts

So both are possible:

• Я люблю...
• Люблю...

Here it describes a general condition/time: when the park is quiet.

It does not refer to one specific moment. Instead, it means something like:

• I like skiing in winter at times when the park is quiet.
• I like skiing in winter, especially when the park is quiet.

Russian когда can introduce:

1. a specific time
   
   • Когда я пришёл, он спал. = When I arrived, he was sleeping.
2. a repeated/general situation
   
   • Я читаю, когда есть время. = I read when I have time.

In this sentence it is the second type: a general repeated situation.

Yes. Russian word order is flexible, though the neutral version here is very natural:

• Я люблю ходить на лыжах зимой, когда в парке тихо.

You could also say:

• Зимой я люблю ходить на лыжах, когда в парке тихо.
• Когда в парке тихо, я люблю ходить на лыжах зимой.

The basic meaning stays similar, but the emphasis changes:

• starting with зимой highlights in winter
• starting with когда в парке тихо highlights the quiet condition

Russian uses word order more for emphasis and information flow than English does, so several versions can be correct.

Often, ходить на лыжах suggests movement across snow rather than downhill skiing, so many learners associate it with cross-country skiing. That is a useful intuition.

Still, in normal speech it can also be understood more generally as to ski. If you want to be more specific, Russian can say:

• беговые лыжи = cross-country skis
• горные лыжи = downhill skis

So:

• Я люблю ходить на беговых лыжах. = I like cross-country skiing.
• Я люблю кататься на горных лыжах. = I like downhill skiing.

In your sentence, without extra detail, it most naturally sounds like ordinary skiing in a park, which many people would picture as cross-country skiing.