Ég set hjólið mitt alltaf í hjólageymsluna af því að það er of kalt úti á veturna.

Set is the present tense, first person singular of setja: ég set = I put / I place.

In this sentence it describes a habitual action, not something happening only once right now:

• Ég set hjólið mitt alltaf ... = I always put my bike ...

So Icelandic present tense often covers both English I put and I am putting, depending on context.

Hjól means bike / wheel / bicycle as a basic noun form.

Hjólið means the bike, because Icelandic usually adds the definite article to the end of the noun instead of using a separate word like English the.

So:

• hjól = a bike / bike
• hjólið = the bike

In this sentence the speaker means a specific bike: my bike.

Both are possible, but they do not feel exactly the same.

• hjólið mitt = my bike, usually referring to a specific, definite bike
• mitt hjól = my bike, but often more indefinite, contrastive, or emphatic

Icelandic very often uses:

• definite noun + possessive

  So hjólið mitt is the most natural choice here.

You can think of it roughly as:

• hjólið mitt = the bike of mine / my bike

Mitt agrees with hjólið in gender, number, and case.

The noun hjól is:

• neuter
• singular

Its possessive must match, so you get:

• minn for masculine
• mín for feminine
• mitt for neuter

Since hjól is neuter, the correct form is mitt.

Alltaf means always. In Icelandic, adverbs like this often come after the verb phrase or after the object, depending on what sounds most natural and what is being emphasized.

So:

• Ég set hjólið mitt alltaf í hjólageymsluna ...

is a natural word order.

If you move alltaf, the meaning stays similar, but the emphasis can shift. Icelandic word order is somewhat flexible, though not completely free.

This is a very common Icelandic case pattern.

With í:

• accusative is usually used for movement toward/into something
• dative is usually used for location inside something

Here the speaker is putting the bike into the bike storage room, so there is movement to a destination:

• í hjólageymsluna = into the bike storage room

Compare:

• Hjólið er í hjólageymslunni. = The bike is in the bike storage room.
• Ég set hjólið í hjólageymsluna. = I put the bike into the bike storage room.

It is a compound noun plus endings.

Base parts:

• hjóla- from hjól = bike
• geymsla = storage room / storage space

Together:

• hjólageymsla = bike storage room / bicycle storage

Then Icelandic adds:

• the definite article
• the case ending needed by the sentence

So:

• hjólageymsla = a bike storage room
• hjólageymslan = the bike storage room (nominative)
• hjólageymsluna = the bike storage room (accusative)

Af því að means because.

It is a very common way to introduce a reason:

• ... af því að það er of kalt ...
• ... because it is too cold ...

You can learn it as a fixed expression. Literally, the parts are not very helpful to translate word-for-word in normal English, so it is best to treat af því að as one chunk meaning because.

This það is a dummy subject, like English it in:

• It is cold
• It is raining

It does not refer to a specific thing. It is just there because Icelandic, like English, usually wants a grammatical subject in this kind of sentence.

So:

• það er kalt = it is cold

Kalt is the neuter singular form of the adjective kaldur = cold.

In weather and impersonal expressions like:

• það er kalt
• það er heitt
• það er dimmt

Icelandic normally uses the neuter singular adjective form.

That is why you get:

• of kalt = too cold

Úti means outside / outdoors.

So:

• það er of kalt úti = it is too cold outside

Without úti, the sentence would still mean that it is too cold, but úti makes it clear that the speaker is talking about outdoor conditions.

Á veturna is an idiomatic Icelandic way to say in winter or during the wintertime.

Yes, it is built with a plural-looking form, and that is normal. Icelandic often uses seasonal expressions like this:

• á veturna = in winter
• á sumrin = in summer
• á haustin = in autumn
• á vorin = in spring

So even though English uses singular in winter, Icelandic commonly uses this fixed seasonal pattern. It does not have to mean several separate winters in a literal sense.

Of means too in the sense of excessively.

So:

• of kalt = too cold

Compare:

• kalt = cold
• mjög kalt = very cold
• of kalt = too cold

So the sentence means not just that it is cold, but that it is cold enough to be a problem.