Learn Hardcore Japanese: huyu ha soto ni deru toki, tebukuro to masuku wo kanarazu tukeru youni site iru. - In winter, when I go outside, I make sure to always wear gloves and a mask.

冬は puts more focus on winter as a general situation (what you do in winter as a rule).
冬に sounds a bit more like one specific time frame (not wrong, but slightly different nuance).

Here, because the sentence describes a habit (what you always do in winter), 冬は fits very naturally as the topic.

Why is it 外に出る and not 外へ出る or 外を出る?

With 出る (to go out / to exit):

The place you go out to is usually marked with に or へ:
- 外に出る
- 外へ出る

Both に and へ are acceptable here. Very roughly:

に is a bit more general and is used a lot with states and destinations.
へ emphasizes the direction a little more (toward outside).

外を出る is ungrammatical in standard Japanese because を with 出る normally marks the place you leave, not the destination:

家を出る = to leave the house
部屋を出る = to leave the room

So:

家を出て、外に出る = I leave the house and go outside.

In your sentence, the important point is the destination outside, so 外に出る is natural.

What is the role of とき in 外に出るとき? How is 出るとき different from 出たとき?

とき means when. The phrase before it modifies とき.

出るとき = when (I) go out / at the time of going out
出たとき = when (I) have gone out / after (I) went out

The nuance:

出るとき refers to the moment right before or while you are going out.
In this sentence, it implies before going out, I (make sure to) put on gloves and a mask.
出たとき refers to the moment after you have already gone out.
That would sound like you only put on gloves and a mask after stepping outside, which isn’t what the sentence wants to say.

So 外に出るとき is used because the action (putting on gloves and a mask) is done in preparation for going out, not after.

How does と work between 手袋 and マスク? Why is there only one を?

と is a listing particle here, like “and”:

手袋とマスク = gloves and a mask

In Japanese, when you have AとBを + verb, the を applies to the entire phrase:

手袋とマスクをつける
= (I) put on gloves and a mask.

You do not say 手袋をとマスクをつける in normal Japanese.
One を at the end is enough to mark both nouns as the direct objects of つける.

What exactly does 必ず mean here? Is it just “always”?

必ず (かならず) means something like:

without fail
definitely
for sure
always (as a rule)

In this sentence, 必ず gives the feeling of a strong rule or commitment:

Not just “I usually wear them”,
but more like “I make sure I always wear them / I never fail to wear them.”

Compared to English, it feels a bit stronger than a simple “I always…” and has a nuance of intention or obligation (a rule you keep to).

Why is the verb つける used for both 手袋 and マスク? I thought gloves use はめる or する.

Japanese has several verbs for putting on / wearing things, and they depend on the item:

着る: clothes on the upper body (shirts, jackets, coats)
履く: things on the legs/feet (pants, shoes, socks)
かぶる: things on the head (hats, helmets)
はめる: rings, gloves, things you insert a body part into
する: accessories in general (ties, necklaces, earrings, masks, gloves, etc.)
つける: to attach / put on (wider usage; often for accessories, masks, gloves, etc.)

For 手袋 and マスク:

You can say:
- 手袋をはめる / 手袋をする / 手袋をつける
- マスクをする / マスクをつける

All are used in real life and typically understood the same way.

つける literally means to attach / to put on (so that it’s in contact with your body), so it works nicely for:

マスク (attached to your face)
手袋 (attached to your hands)

So 手袋とマスクをつける is natural and idiomatic.

What does 〜ようにしている mean in つけるようにしている? How is it different from just つけている or つける?

〜ようにしている is a useful pattern:

[dictionary form verb] + ようにしている
= to make an effort to do X / to make it a habit to do X / to try to always do X

So:

手袋とマスクをつけるようにしている
≈ I make sure to wear gloves and a mask / I try to always wear gloves and a mask / I’ve made it a habit to wear them.

Compare:

つけている
- Usually means I am wearing them (right now) or I habitually wear them (depending on context).
- 冬は外に出るとき、手袋とマスクをつけている。
  → could mean When I go out in winter, I wear gloves and a mask (a simple habitual statement), but it lacks the “trying / effort / rule” nuance.
つける (plain present)
- Simple habit or general fact:
  - 冬は外に出るとき、手袋とマスクをつける。
    = When I go out in winter, I wear gloves and a mask.
つけるようにしている
- Adds the nuance of conscious effort / self-imposed rule:
  - I make it a point to wear gloves and a mask.

So ようにしている suggests the speaker is intentionally maintaining a habit, not just describing what happens.

What is the function of している in ようにしている? Is it a continuous tense?

Yes, している here is the progressive / continuous form of する, but its meaning is a little idiomatic.

つけるようにする = (I) will try to wear them / will make a point of wearing them (one-time or future decision).
つけるようにしている = (I) am in the state of habitually trying to wear them / I keep doing that.

So している shows that:

This is not a one-time effort,
but an ongoing habit / continuing effort.

Thus, the whole phrase means I habitually make sure to wear them.

Can 必ず go in a different place, like 必ず手袋とマスクをつける? Does the position change the meaning?

In this sentence, 必ず is placed before the verb phrase:

手袋とマスクを必ずつけるようにしている。

You could also say:

必ず手袋とマスクをつけるようにしている。

Both are grammatical and very close in meaning. The nuance is very slight:

手袋とマスクを必ずつけるようにしている。
→ Slight emphasis on 必ずつける (the action of always wearing).
必ず手袋とマスクをつけるようにしている。
→ Slight emphasis that what you definitely wear is gloves and a mask.

In everyday conversation, they are effectively interchangeable; word order for adverbs like 必ず is fairly flexible as long as it is near the verb phrase.

Why is there a comma after とき: 外に出るとき、手袋…? Is it required?

The comma (、) in Japanese is largely about readability and pause, not strict grammar.

外に出るとき、手袋とマスクを…
The comma marks the end of the “when I go outside” clause and separates it from the main action.

You could also write:

冬は外に出るとき手袋とマスクを必ずつけるようにしている。

Without the comma, it is still grammatical, but slightly harder to read, especially for learners. Native writers often put a comma after a 〜とき clause because that’s where a natural pause comes in.

Is the whole sentence polite, casual, or neutral? How would it look in a casual style?

The sentence ends with している (plain form), not しています, so grammar-wise it is plain / neutral form.

However, plain form can be:

Casual between friends,
Or neutral / written in diaries, essays, etc.

A clearly casual spoken version might also drop some particles:

冬は外出るとき、手袋とマスク必ずつけるようにしてる。

A more polite version (e.g., talking to a stranger or in customer service) would use 〜しています:

冬は外に出るとき、手袋とマスクを必ずつけるようにしています。

So the original sentence is plain form, appropriate for writing, inner monologue, or talking to someone in a non-formal setting.

Could 冬は be omitted? What would happen if I just said 外に出るとき、手袋とマスクを必ずつけるようにしている。?

Yes, it’s possible:

外に出るとき、手袋とマスクを必ずつけるようにしている。
= When I go outside, I make sure to wear gloves and a mask.

Without 冬は, the sentence no longer limits the habit to winter; it sounds like a general rule, all year round.

With 冬は:

It clearly means “In winter (as for winter), when I go out, I make sure to wear them.”

So whether you include 冬は or not changes when this habit applies.