Zimą noszę gruby sweter w domu.

Because zimą is the form Polish uses here to mean in winter.

The basic dictionary form is zima = winter.
In this sentence, Polish uses the instrumental singular: zimą.

With seasons, this is very common:

• wiosną = in spring
• latem = in summer
• jesienią = in autumn
• zimą = in winter

So Zimą noszę... means In winter, I wear...

Because nosić means to wear in the sense of having something on regularly or habitually.

That fits this sentence well: In winter I wear a thick sweater at home.

Compare:

• nosić = to wear
• zakładać / założyć = to put on
• ubierać się / ubrać się = to get dressed

So:

• Zimą noszę gruby sweter = In winter I wear a thick sweater
• Zakładam gruby sweter = I am putting on a thick sweater

Noszę is:

• 1st person singular
• present tense
• from nosić

So it means I wear or sometimes I am wearing, depending on context.

Because the sentence has Zimą at the start, it sounds like a habit or general routine, not just something happening right now.

They do match grammatically, but in this case the forms happen to look like the basic ones.

• sweter = sweater
• gruby = thick

After noszę in an affirmative sentence, sweter is the direct object, so it goes into the accusative case.

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

So:

• nominative: gruby sweter
• accusative: gruby sweter

That is why nothing visibly changes here.

W domu means at home or in the house.

Here, w means in, and because this is a location (not movement), Polish uses the locative case.

So:

• dom = house / home
• w domu = in the house / at home

A useful contrast:

• w domu = at home, in the house
• do domu = to the house, home

So:

• Jestem w domu = I am at home
• Idę do domu = I’m going home

It can mean either, depending on context.

In everyday Polish, w domu very often means at home, not just physically inside a building.

So in this sentence, the most natural understanding is: At home, I wear a thick sweater in winter.

Yes. Polish word order is more flexible than English word order.

The sentence Zimą noszę gruby sweter w domu is natural and neutral, with emphasis starting on in winter.

You could also say:

• W domu noszę zimą gruby sweter
• Gruby sweter noszę zimą w domu

These are grammatical, but the emphasis shifts.

In general:

• putting Zimą first highlights the time
• putting gruby sweter first highlights what you wear
• putting w domu first highlights the place

English usually has less freedom here.

Because Polish has no articles.

English uses:

• a thick sweater
• the thick sweater

Polish does not have separate words for a/an/the.
So gruby sweter can mean:

• a thick sweater
• the thick sweater

The exact meaning depends on context.

Most naturally, it describes a habit or general fact:

In winter, I wear a thick sweater at home.

That is because:

• noszę is present tense
• Zimą gives a general time frame

If you specifically wanted to stress what you are wearing right now, Polish often uses a different phrasing, for example:

• Mam na sobie gruby sweter. = I have a thick sweater on.
• Mam na sobie gruby sweter w domu. = I’m wearing a thick sweater at home.

So noszę here sounds more like a regular winter habit.

A rough guide:

• zimą ≈ ZEE-mom
• noszę ≈ NO-sheh (with a nasal final vowel)

A few helpful sound notes:

• z in zimą sounds like English z
• sz in noszę sounds like English sh
• ą is a nasal vowel; at the end of a word it is often heard roughly like om
• ę at the end of a word is often pronounced weakly; in careful speech it is nasal, but in everyday speech it may sound less strongly nasal

So an English speaker can start with:

• ZEE-mom
• NO-sheh

That will be understood, even if the exact Polish nasal vowels take practice.