En hiver, le bébé reste dans sa poussette même quand mon fils court partout.

En hiver is the normal French way to say in winter when you mean the season in a general sense.

• en été = in summer
• en hiver = in winter
• au printemps = in spring
• en automne = in autumn

Dans l’hiver would sound unusual here. It might only appear in a more literary or very specific context, not in an ordinary sentence like this.

Le bébé means the baby, while un bébé means a baby.

French often uses the definite article when the speaker has a specific person or thing in mind, even if English might sometimes be looser about it. Here, it sounds like the speaker is talking about a particular baby that is known in the situation, so le bébé is natural.

Here, reste comes from rester, which often means to stay or to remain.

So le bébé reste dans sa poussette means the baby stays in the stroller / pushchair.

It does not mean that the baby is actively going somewhere. It suggests staying in that place rather than moving around.

Dans means in or inside, so dans sa poussette means in his/her stroller.

French uses dans naturally with things like seats, vehicles, containers, or enclosed spaces. A stroller is treated as something the baby is sitting in, so dans is the normal preposition.

This is a very common question.

In French, possessive adjectives agree with the thing possessed, not with the owner.

Here:

• poussette is a feminine noun
• so the possessive must be sa

That is true whether the stroller belongs to a boy, a girl, or simply the baby.

So:

• son livre = his/her book, because livre is masculine
• sa poussette = his/her stroller, because poussette is feminine

Même quand means even when.

It introduces a contrast:

• the baby stays in the stroller
• even when my son runs everywhere

So the idea is that the baby remains in the stroller despite the more chaotic situation around him/her.

No. They look similar, but they mean different things.

• même quand = even when
• quand même = all the same, anyway, still

Examples:

• Même quand il pleut, il sort. = Even when it rains, he goes out.
• Il pleut, mais il sort quand même. = It’s raining, but he goes out anyway.

So in your sentence, même quand is the correct expression.

Court is the third-person singular present tense form of courir = to run.

Conjugation in the present:

• je cours
• tu cours
• il/elle/on court
• nous courons
• vous courez
• ils/elles courent

Since mon fils = my son = he, French uses court.

Partout means everywhere or all over the place.

So mon fils court partout gives the idea that the son is running around in many places, not staying still.

It often adds a sense of energetic or uncontrolled movement:

• Les enfants courent partout. = The children are running everywhere.

French often uses the present tense to describe:

• something happening now
• a general truth
• a habit or usual situation

In this sentence, the present tense can sound like a general or typical situation: In winter, the baby stays in the stroller even when my son runs everywhere.

So it may describe what usually happens, not just one single moment.

The comma separates the introductory time phrase En hiver from the rest of the sentence.

This is similar to English:

• In winter, ...

The comma is not always absolutely required in every short French sentence, but it is very natural and helps readability here.

Yes, grammatically you could say même lorsque, because lorsque also means when.

However, quand is more common and more natural in everyday speech.
Lorsque often sounds a bit more formal or written.

So:

• même quand mon fils court partout = very natural everyday French
• même lorsque mon fils court partout = correct, but more formal

A rough pronunciation guide is:

mon fils court partout → mohn fees koor par-too

A few useful notes:

• fils is usually pronounced fees here
• court sounds like koor
• the final t in court is normally silent
• partout sounds like par-too

Also, French rhythm is smoother than English, so the words flow together more evenly.