Do so and such mean anything different?

No, the meaning is identical and only the grammar differs. Such a cold day and so cold a day say the same thing, which is why the choice feels arbitrary. It is purely structural, decided by whether a noun follows.

What is the that clause for?

It states the result: it was so cold that we went home, it was such a mess that we started again. In speech the that is usually dropped. It was so cold we went home, and the sentence is no less correct for it.

Is “so fun” acceptable?

It is common in speech and disliked in formal writing, because fun was traditionally a noun, hence such fun. So much fun is the safe form everywhere. Language is shifting here, but an exam will still prefer the traditional version.

Which one to useB1

So vs such

The short answer

So goes with an adjective or adverb on its own: it was so cold. Such goes with a noun phrase: it was such a cold day. If there is a noun after the adjective, you need such, and the article moves after it, giving such a rather than a such.

At a glance

So or Such?

Compare	SoAdjective or adverb, with no noun.	SuchA noun phrase, with or without an adjective.
What follows	so + adjective / adverb	such + (a) + adjective + noun
Article	Not used	such a, before a singular countable noun
Plural nouns	Not used	such good results: no article
Uncountable nouns	Not used	such bad weather: no article
With many, much, few	so many, so much, so few	Not used
Result clause	so cold that we left	such a cold day that we left

How to choose

Ask these, in order

1
Is there a noun after the adjective?
Such. The noun is what pulls it.
It was such a long meeting.
Meeting is a noun, so such.
2
Is the adjective standing alone?
So.
The meeting was so long.
No noun after long.
3
Is the next word many, much, few or little?
So, always. These four are the exception to the noun rule.
There were so many people.
A noun follows, and it is still so.
NBSuch many is never correct.
4
Where does the article go?
After such, never before: such a good idea.
She gave such a clear answer.
A such clear answer is not English.

Side by side

Each one, in full

When to use so

Adjective or adverb, with no noun.

So intensifies an adjective or an adverb standing on its own, so tired, so quickly, so expensive. There is no article and no noun, and adding one forces the switch to such.

It also pairs with the four quantifiers many, much, few and little, which behave as a set, so many mistakes, so much noise, so few options, so little time. That is the one place a noun can follow so.

I was so tired I fell asleep on the train.

Adjective alone.

It happened so quickly nobody reacted.

Adverb.

There’s so much to do before Friday.

So with much, the quantifier exception.

Such

When to use such

A noun phrase, with or without an adjective.

Such introduces a noun phrase, with or without an adjective inside it: such a mess, such a good film, such interesting people. The article sits after such when the noun is singular and countable.

With plural or uncountable nouns there is no article at all: such good results, such bad weather, such nonsense. Learners often insert one by analogy with the singular, and it is the commonest error after the a-placement.

It was such a relief to finish.

Singular countable, so such a.

They asked such difficult questions.

Plural, so no article.

We had such awful luck that week.

Uncountable, so no article.

Mistakes to avoid

What learners actually get wrong

It was a such good film.
It was such a good film.
The article goes after such, not before it. This is a word-order error rather than a choice error, and it is the single most common mistake with the pair.
It was so a cold day.
It was such a cold day. / It was so cold.
A noun after the adjective forces such. Both repairs work. One keeps the noun, the other drops it, but so can never sit in front of an article.
There were such many people.
There were so many people.
Many, much, few and little take so despite being followed by nouns. They behave as quantifiers rather than as ordinary adjectives, which is why they break the pattern.
They gave us such good advices.
They gave us such good advice.
Advice is uncountable in English, so it takes no article and no plural. The such is correct here, the noun is what went wrong.

Questions

Asked and answered

Do so and such mean anything different?: No, the meaning is identical and only the grammar differs. Such a cold day and so cold a day say the same thing, which is why the choice feels arbitrary. It is purely structural, decided by whether a noun follows.
What is the that clause for?: It states the result: it was so cold that we went home, it was such a mess that we started again. In speech the that is usually dropped. It was so cold we went home, and the sentence is no less correct for it.
Is “so fun” acceptable?: It is common in speech and disliked in formal writing, because fun was traditionally a noun, hence such fun. So much fun is the safe form everywhere. Language is shifting here, but an exam will still prefer the traditional version.