Зимой мой муж уезжает затемно, а я стараюсь хотя бы по выходным гулять засветло.

Because Russian often uses the instrumental case by itself to express seasons and some time words adverbially.

So:

• зимой = in winter
• летом = in summer
• весной = in spring
• осенью = in autumn

The base noun is зима, and зимой is its instrumental singular form. In this use, it functions almost like an adverb.

Russian uses the present tense of imperfective verbs for habitual or repeated actions.

So мой муж уезжает затемно does not mean he is leaving right now. It means something like:

• he usually leaves while it is still dark
• this is his regular winter habit

This is very common in Russian:

• По утрам он пьёт кофе = He drinks coffee in the mornings
• Зимой мы рано ложимся спать = In winter we go to bed early

These verbs are related, but not identical.

• уходить = to leave, to go away, often on foot or in a general sense
• уезжать = to leave by transport, to drive away, ride away, or go away some distance

So уезжает suggests that the husband is departing by car, train, bus, or some other means of transport, or at least that Russian conceptualizes his departure that way.

If he were simply stepping out or walking away, уходит might be more natural.

These are fixed adverbs connected with light and darkness.

• затемно = while it is still dark, usually before dawn
• засветло = while it is still still light, usually before nightfall

So the contrast is very neat:

• the husband leaves before it gets light
• the speaker tries to walk before it gets dark

They are best learned as whole adverbs. A useful pronunciation note:

• зате́мно
• засве́тло

They are perfectly understandable and natural, but they do have a slightly idiomatic or bookish flavor compared with more explicit phrases like:

• когда ещё темно
• пока ещё светло

That said, they are still widely used, especially in written Russian and careful speech.

Хотя бы means at least.

It adds the idea of a minimum goal or limited success:

• maybe not every day
• maybe not whenever she wants
• but at least on weekends

So я стараюсь хотя бы по выходным гулять засветло implies a small but realistic effort.

По выходным is a very common way to say on weekends in the sense of habitually or every weekend.

Here is the difference:

• по выходным = on weekends, as a repeated pattern
• в выходные = on the weekend / during the weekend, often more tied to a particular weekend or used more loosely

So in this sentence, по выходным fits well because the speaker is talking about a routine.

Grammatically, выходным is the dative plural after по. The expression comes from something like по выходным дням.

Because the speaker is talking about a general repeated activity, not one completed walk.

• гулять = to walk, stroll, be out walking, go for walks
• погулять = to take a walk for a while, often as a single bounded event

After стараюсь, the imperfective often sounds more natural when describing a habit or ongoing intention:

• стараюсь читать по-русски
• стараюсь больше спать
• стараюсь гулять по вечерам

So гулять here means she tries to make walking in daylight part of her routine, at least on weekends.

Because the dictionary form is стараться, which simply means to try or to make an effort.

The -ся is just part of the verb. It does not translate literally as a reflexive English meaning like try oneself.

A very common pattern is:

• стараться + infinitive

For example:

• Я стараюсь говорить медленно
• Мы стараемся не опаздывать
• Она старается больше отдыхать

So я стараюсь гулять = I try to go for walks.

Russian word order is flexible, and the infinitive often comes after the words that modify it.

In this sentence, хотя бы по выходным is placed before гулять because it carries important emphasis:

• the speaker cannot always do this
• but she tries to do it at least on weekends

So the order helps spotlight the limitation before the action itself.

A different word order could be possible, but this one sounds natural and well balanced.

Yes, Russian often can omit possessive words like мой with family members when the meaning is obvious.

For example:

• Муж уже пришёл
• Жена работает дома

But мой муж is still completely natural here. It helps:

• identify the person clearly
• create a contrast with я
• make the two halves of the sentence feel balanced: мой муж ..., а я ...

So мой is not strictly necessary, but it works very well stylistically.

Because а joins two separate clauses with different subjects:

• мой муж уезжает затемно
• я стараюсь хотя бы по выходным гулять засветло

In Russian, that normally requires a comma.

Also, а often signals contrast or comparison, not just simple addition. Here the contrast is clear:

• he leaves in darkness
• I try to walk in daylight

So the comma is both grammatically required and rhetorically natural.