Learn Hardcore German: Im Winter trage ich hohe Stiefel, damit meine Füße trocken bleiben. - In winter I wear high boots so that my feet stay dry.

Im is a contraction of in dem. Literally, im Winter = in dem Winter = in the winter.
We almost always use the contracted form im in speech and writing.
You’d normally only say in dem Winter if you really want to emphasize a particular winter, for example:

In dem Winter 1945 war es sehr kalt. – In that winter of 1945 it was very cold.
In your sentence, Im Winter just means in (the) winter in a general, habitual sense.

Which case is “Winter” in, and why?

Winter is in the dative case.
The preposition in can take accusative or dative; with time expressions like seasons, it normally takes dative.
Because Winter is masculine, in + dem Winter becomes im Winter.
So: in (dem) Winter → dative masculine → im Winter.

Why does the sentence start with “Im Winter trage ich …” instead of “Ich trage im Winter …”? Is there a difference?

Both are correct:

Im Winter trage ich hohe Stiefel.
Ich trage im Winter hohe Stiefel.

German likes the time–manner–place order, and putting the time element (Im Winter) first is very common.
When you move Im Winter to the start, it takes the first position in the sentence, so the verb trage must still be in second position, which forces ich after the verb: Im Winter trage ich ….
The meaning is the same; Im Winter trage ich … puts a bit more emphasis on when you wear the boots.

What does “trage” mean here, and why not “habe … an” or something else?

tragen means “to wear” (for clothes, shoes, accessories) and also “to carry”.
ich trage = I wear / I am wearing.
Other options:

Ich habe hohe Stiefel an. – I am wearing high boots (right now).
Ich ziehe hohe Stiefel an. – I put on high boots.

In your sentence, trage expresses a habit (what you usually wear in winter), so it’s a good, natural choice.

Why is it “hohe Stiefel” and not “hohen Stiefel” or “hohe Stiefeln”?

hohe Stiefel is accusative plural with no article.

The verb tragen takes a direct object → accusative: I wear what? → hohe Stiefel.
Stiefel is plural, and in the plural with no article (kein, mein, etc.), the adjective ending for accusative is -e: hohe.

So the pattern is:

Ich trage hohe Stiefel. (plural, no article → hohe)
Forms like hohen Stiefel or hohe Stiefeln would be grammatically wrong here.

What gender and plural does “Stiefel” have?

Stiefel (boot) is masculine: der Stiefel.
Its plural is also “Stiefel” (no extra ending):

Singular: der Stiefel – the boot
Plural: die Stiefel – the boots

You know it’s plural in your sentence because of the adjective hohe (and the context).

Why is “Stiefel” plural here? Could I say it in the singular?

You can use both, but they mean slightly different things:

Ich trage hohe Stiefel. – I wear high boots. (in general, meaning a pair of boots)
Ich trage einen hohen Stiefel. – I wear one high boot. (very unusual, unless you really mean only one boot)

In German, when talking about what you usually wear on your feet, you normally use the plural: Schuhe, Stiefel, Socken, etc.

Why is there a comma before “damit”?

In German, you must put a comma before a subordinate clause.
damit meine Füße trocken bleiben is a subordinate clause (Nebensatz) introduced by the subordinating conjunction damit.
So the comma marks the boundary between the main clause:

Im Winter trage ich hohe Stiefel,
and the subordinate clause:
damit meine Füße trocken bleiben.

What does “damit” mean here, and how is it different from “weil” or “um … zu”?

Here damit means “so that / in order that” and expresses purpose / intention:

Ich trage hohe Stiefel, damit meine Füße trocken bleiben.
→ I wear high boots so that my feet stay dry.

Differences:

weil = because → gives a reason, not a purpose:
- Ich trage hohe Stiefel, weil es regnet. – because it’s raining.
um … zu = in order to → also purpose, but used when the subject is the same in both parts:
- Ich trage hohe Stiefel, um meine Füße trocken zu halten.
  (subject “ich” in both parts)

With damit, the subject can be different; here it changes from ich to meine Füße.

Why does the verb “bleiben” go to the end in “damit meine Füße trocken bleiben”?

damit is a subordinating conjunction (like weil, dass, wenn).
Subordinating conjunctions send the conjugated verb to the end of the clause.
So the normal word order is:

[damit] [subject] [the rest] [verb at the end]
In your sentence:
damit – conjunction
meine Füße – subject
trocken – predicate adjective
bleiben – conjugated verb at the end

Hence: damit meine Füße trocken bleiben.

Why is it “meine Füße” and not “meinen Füßen” or something else?

In the damit clause, meine Füße is the subject → so it takes the nominative case.

Wer / was bleibt trocken? – Who / what stays dry? → meine Füße.

Nominative plural of mein is meine, and the noun is Füße (plural of Fuß):

Singular: mein Fuß – my foot
Plural: meine Füße – my feet

meinen Füßen would be dative plural (e.g. mit meinen Füßen), which is not needed here.

Why does “Füße” have an umlaut? What is the singular?

The singular is der Fuß – the foot.
The plural adds -e and gets an umlaut: Füße – feet.
This is a common pattern with some masculine nouns:

der Stuhl → die Stühle – chair(s)
der Schuh → die Schuhe – shoe(s) (no umlaut here)
der Fuß → die Füße – foot/feet

So meine Füße simply means my feet.

Why is “trocken” not “trockene” or “trockenen”?

Here trocken is a predicate adjective (it comes after the verb bleiben and describes the subject).
Predicate adjectives in German do not get endings; they stay in the base form:

Die Füße sind trocken. – The feet are dry.
Die Füße bleiben trocken. – The feet stay dry.

Adjective endings like trockene, trockenen, etc. are used before nouns:

trockene Füße – dry feet (attributive, before noun).

Why is the present tense “trage” used? In English I might say “I wear” or “I usually wear”.

German present tense (ich trage) covers both:

simple present – I wear
present progressive / habitual – I am wearing, I usually wear

Context tells you it’s a habit: it’s about what you generally do in winter.
So Im Winter trage ich hohe Stiefel naturally means “In winter I (usually) wear high boots.”
You don’t need a special tense or extra word to show the habitual meaning.

Can I put the “damit” clause first, like “Damit meine Füße trocken bleiben, trage ich im Winter hohe Stiefel”?

Yes, that’s perfectly correct and quite natural:

Damit meine Füße trocken bleiben, trage ich im Winter hohe Stiefel.

If you put the subordinate clause first, it all counts as position 1, so in the following main clause the verb still must be in second position:

…, trage ich … (not ich trage).
The meaning is the same; starting with Dam it … puts more emphasis on the purpose.

Could I use “sodass” instead of “damit”, and what would change?

You could say:

Im Winter trage ich hohe Stiefel, sodass meine Füße trocken bleiben.

sodass focuses more on a result (so that / with the result that) rather than on an intended purpose.

damit → I wear high boots in order to keep my feet dry (intention).
sodass → I wear high boots, with the result that my feet stay dry (outcome).

In everyday speech, the difference is subtle; damit is the more typical choice for purpose.