На каток мы поедем в субботу, если мама найдёт мои тёплые варежки.

Russian often uses на with places seen as venues, activities, or open/public spaces.
So на каток means to the skating rink.

Compare:

• на каток — to the rink
• на стадион — to the stadium
• на концерт — to the concert

By contrast, в is more typical for going into an enclosed space or institution:

• в школу — to school
• в магазин — to the store
• в дом — into the house

So here на каток is just the normal Russian choice.

Поедем comes from поехать, which means to go by transport: by car, bus, train, etc.

Пойдём comes from пойти, which means to go on foot.

So:

• мы поедем = we’ll go (by vehicle)
• мы пойдём = we’ll go (walking)

The sentence suggests they will travel there rather than walk.

Because поедем is the simple future form of the perfective verb поехать.

In Russian:

• imperfective verbs form the future with быть
  • infinitive
    
    • будем ехать
• perfective verbs have a simple future form
  
  • поедем

Here поехать is perfective and refers to one completed trip/event, so поедем means we will go.

To say on Saturday, Russian uses в + accusative with days of the week.

So:

• в субботу — on Saturday
• в понедельник — on Monday
• в среду — on Wednesday

This is the normal pattern for saying when something happens on a particular day.

This is a very common difference between English and Russian.

In Russian, when the condition is about the future, the verb after если is normally also in the future:

• Если мама найдёт варежки, мы поедем.

Literally it looks like:

• If Mom will find the mittens, we will go.

But this is standard Russian grammar. English avoids will after if, while Russian does not.

So in future real conditions, Russian often has:

• если + future, future

Найдёт is the 3rd person singular future form of найти (to find).

So:

• я найду — I will find
• ты найдёшь — you will find
• она найдёт — she will find

Here мама найдёт means Mom will find.

Also, the letter ё shows the stress: найдёт.

Yes, it is accusative, because these are the direct object of найдёт.

However, in Russian, plural inanimate nouns have the same form in the accusative as in the nominative.

So:

• nominative: мои тёплые варежки
• accusative: мои тёплые варежки

That is why the phrase looks unchanged.

Everything agrees in plural:

• мои — my (plural)
• тёплые — warm (plural)
• варежки — mittens (plural)

Both are things you wear on your hands, but they are different:

• варежки = mittens
  Fingers are together.
• перчатки = gloves
  Each finger has its own section.

So тёплые варежки are specifically warm mittens, not gloves.

Yes, Russian often omits subject pronouns when they are clear from the verb form.

So both are possible:

• На каток поедем в субботу...
• На каток мы поедем в субботу...

Including мы can add a slight sense of emphasis, contrast, or clarity, something like:

• As for us, we’ll go to the rink on Saturday...

It is not required, but it sounds natural.

Russian word order is flexible. The sentence could be rearranged in several ways without changing the basic meaning:

• Мы поедем на каток в субботу, если мама найдёт мои тёплые варежки.
• Если мама найдёт мои тёплые варежки, мы поедем на каток в субботу.
• В субботу мы поедем на каток, если мама найдёт мои тёплые варежки.

The chosen order puts На каток first, which gives it some emphasis and sets the scene early.

Russian often moves parts of the sentence around for focus, emphasis, or style.

Because если мама найдёт мои тёплые варежки is a subordinate clause introduced by если (if).

Russian normally separates this kind of clause with a comma:

• ..., если ...
• Если ..., ...

So the comma here is required.

Тёплые agrees with варежки in number, gender, and case.

Since варежки is:

• plural
• inanimate
• here in the accusative (same as nominative for plural inanimate)

the adjective must also be plural in the matching form:

• тёплые варежки — warm mittens

So the phrase is fully matched:

• мои — plural
• тёплые — plural
• варежки — plural

Yes. In everyday Russian writing, ё is often written as е, so you may see:

• найдёт
• найдет

They usually mean the same word, and native speakers understand it from context.

But for learners, ё is very helpful because it shows the correct pronunciation and stress:

• найдёт, not нАйдет or найдЕт