Re: Because, as, since
There is often no real difference between the three words, and I agree with emsr2d2 that all your sentences are acceptable.
Clauses with 'as' and 'since' often begin the sentence, and often contain information that is known to the listener:
Since/As it was snowing heavily, the guests had decided to postpone their departure.
Clauses with 'because' often introduce new information, and often follow the main clause:
The guests had decided to postpone their departure, because it was snowing heavily.
Because-clauses, but not as- and if-clauses can stand alone in answer to a question:
Why had the guests had decided to postpone their departure?
Because it was snowing heavily.
Context is always important; labelling is rarely important.