Being a holiday (1)/ we went out (2)/ for a picnic. (3)/ No error. (4)

Answer

1

Explanation

It being a holiday will replace being a holiday Combination of two/more sentences is possible only when the sentences have a common Subject.
Look at the examples given below:
I read the book. I returned it to the library.
Combining the two sentences we get -
Having read the book I returned it to the library (right)
Reading the book I returned it to the library. (wrong)
Another example -
It was a rainy day. I could not go.
It being a rainy day I could not go.