Questions & Answers about Зимой я ношу тёплый шарф и варежки.
Зимой is the instrumental singular of зима (winter), but here it is being used adverbially to mean in winter / during winter.
This is very common with seasons in Russian:
- зимой — in winter
- весной — in spring
- летом — in summer
- осенью — in autumn
So Russian often says simply зимой, without a preposition, where English uses in.
You can leave it out.
Russian often drops subject pronouns when they are clear from the verb ending.
Ношу already means I wear / I carry, so:
- Зимой я ношу тёплый шарф и варежки.
- Зимой ношу тёплый шарф и варежки.
Both are natural.
Including я can make the subject a little clearer or more emphatic, especially if you are contrasting yourself with someone else.