What's the purpose of な in なのに?

Question

I don't understand the role of "な" when used before "のに" as in these two sentences (with given translations):

朝目がさめて初めて、外が雪なのに気がついた。

He noticed that there was snow outside only after he woke up in the morning.

せっかくの日曜日なのに働いた。

Although Sunday is precious (to me), I worked (all day long).

I'm similarly confused by the なので pattern, but I assume the principle is the same there. My best guesses so far are that:

1. There's some relation to な-adjectives, but I don't see how 雪 or 日曜日 would be acting as adjectives here.
2. The な has essentially the same role as だ (i.e. a "copula"?), but you can't use だ in the middle of a sentence like that.

Answer 1

You are on the right track. の is a formal noun with a general meaning such as the case, the fact, or the situation. The sequence ...な is an appositive clause modifying the formal noun の.

彼は学生だ
'He is a student.'

[彼は学生な]のだ
'It is the case [that he is a student].'
The appositive clause 彼は学生な 'that he is a student' modifies the formal noun の 'the case'.

As you suspect, な is the form of copula that is used exclusively when it is used in a clause that modifies a noun (i.e., relative clause or appositive clause).

彼は静かだ
'He is quiet.'

[静かな]人
'person [who is quiet]' (relative clause with na-adjective as a predicate)

Na-adjectives are actually very close to nouns, and depending on the theoretical framework, they can be actually considered a subclass of noun. You can usually observe this な form used together with na-adjevtives, but with nouns, you don't usually see it except for a number of fixed expressions like the one you see here because with nouns, you have the option of using the genitive case particle の, and that is preferred.

彼は学生だ
'He is a student.'

× [学生な]人
'person [who is a student]' (relative clause with a noun as a predicate; usually considered ungrammatical to use な)

学生の人
(Uses genitive case particle)

Answer 2

First, the two のに are completely different.

外が雪なのに気がついた。

そとが+雪+な+の+に気づく

の is used to make a noun of the preceding proposition, so as to make the proposition the object of 気づく (object indicated by に).
But then, a proposition cannot end with a noun, it must end with a verb, and 雪 is not a verb. The proposition is in fact そとが雪だ。 And when you put だ in determinant form (so that it determines の) you turn it into な. That's it.
To realise [the fact that [outside is snow]]

日曜日なのに働いた。

This is a "grief" のに, and also goes with a proposition, not a noun. Your proposition is 日曜日だ. You turn だ into な, and you can now stick のに behind it.

So, your point 1 is wrong.
Your point 2 is right, and turning だ into な is a solution.

なので will work similarly, and be like the second example (since ので and the second のに are single grammatical particles).