После работы мы пошли на каток, хотя уже начиналась метель.

Because после requires the genitive case in Russian.

• Base form: работа = work, job
• Genitive singular: работы

So после работы means after work or after the workday.

This is a very common pattern:

• после урока = after the lesson
• после обеда = after lunch
• после фильма = after the movie

Пошли is the perfective past of пойти, and here it means we went / we set off.

The difference is:

• шли = were going, were on the way, went in a process-oriented sense
• пошли = started going, set off, went as a completed action

In this sentence, the speaker is describing a completed event: after work, we went to the skating rink. That is why пошли is the natural choice.

If you said После работы мы шли на каток, it would sound more like After work we were walking/going to the skating rink, focusing on the process rather than the fact that they went there.

In Russian, some destinations are used with на, and каток is one of them.

So the normal expression is:

• идти на каток = to go to the skating rink

This is similar to other common Russian patterns:

• идти на работу = go to work
• идти на концерт = go to a concert
• идти на стадион = go to the stadium

By contrast, в is used with many enclosed places:

• идти в школу = go to school
• идти в магазин = go to the store
• идти в парк = go into the park

So this is something you often just learn as part of the noun’s normal usage.

It actually is in the accusative case, because motion toward a destination with на uses the accusative.

But каток is a masculine inanimate noun, and for masculine inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• Nominative: каток
• Accusative: каток

That is why there is no visible change.

Compare with a feminine noun, where you would see the change more clearly:

• на работу from работа
• в школу from школа

Because хотя introduces a subordinate clause meaning although / even though.

Russian normally puts a comma before subordinate clauses of this kind:

• Мы пошли на каток, хотя уже начиналась метель.

This is similar to English:

• We went to the skating rink, although a snowstorm was already beginning.

So the comma is standard punctuation here.

Хотя means although, though, or even though.

It introduces a contrast:

• Мы пошли на каток = we went to the skating rink
• хотя уже начиналась метель = although a snowstorm was already beginning

So the idea is: they went anyway, despite the bad weather starting.

A few similar examples:

• Он вышел, хотя было поздно. = He went out although it was late.
• Мы поехали, хотя шёл дождь. = We left/go anyway although it was raining.

Начиналась is imperfective, while началась is perfective.

Here, начиналась means was beginning or was starting. It presents the snowstorm as a process that was already underway at that moment.

• начиналась метель = a snowstorm was beginning
• началась метель = a snowstorm began / started

In this sentence, the imperfective form works well because it gives background to the main action:

• Мы пошли на каток = main event
• хотя уже начиналась метель = background situation developing at that time

If you used началась, the meaning would shift slightly toward a more definite completed start: although a snowstorm had already started.

Both can be possible in some contexts, but начиналась emphasizes the unfolding situation.

Because the verb agrees with метель, which is a feminine singular noun.

• метель = snowstorm, blizzard
• feminine singular noun
• therefore past tense verb: начиналась

In Russian past tense, verbs agree in gender and number:

• masculine: начинался
• feminine: начиналась
• neuter: начиналось
• plural: начинались

Since метель is feminine singular, начиналась is the correct form.

Yes, Russian could leave it out:

• После работы пошли на каток...

Because пошли already shows 1st person plural (we went), the subject is grammatically clear.

However, Russian often includes pronouns like мы when the speaker wants:

• clarity
• contrast
• a more explicit subject
• a more natural rhythm

So мы is not required, but it is completely normal.

No, Russian word order is fairly flexible.

This sentence uses:

• хотя уже начиналась метель

But you could also see:

• хотя метель уже начиналась

Both are grammatical.

The difference is mostly about emphasis and flow. In the original version, the sentence feels natural and slightly more focused on the fact that the snowstorm was already starting. Putting метель later can make it sound a little more dramatic or informationally balanced.

Russian word order often depends on what is treated as known information and what is being highlighted.

Уже means already, and in Russian it is often placed near the word or phrase it modifies.

Here:

• уже начиналась = was already beginning

That placement sounds natural because уже modifies the action of beginning.

You might also hear:

• хотя метель уже начиналась

That is also correct. Russian allows some flexibility, but уже начиналась метель is very natural in this sentence.

Because Russian has no articles.

English says things like:

• after work
• to the skating rink
• a snowstorm

Russian simply uses the noun without a/an/the:

• после работы
• на каток
• метель

Whether something is the, a, or just general is understood from context.

That is one of the biggest structural differences between Russian and English.