You have to be clear whether you are using 'picnic' as a noun or a verb in your sentence. It can be either.

The most common phrase is 'go for a picnic', or 'go on a picnic' if is a larger and more organised event. In these phrases, the word 'picnic' is a noun, and you need the article 'a'.

It is also correct, but slightly less common, to use 'picnic' as a verb.

So, for example, if you say 'We're going to picnic in the woods', 'going to picnic' is a verb form. 'are going to' indicates a future plan, and 'picnic' is the main verb.

This is different grammatically from 'We're going for a picnic in the woods'. In this sentence, 'are going to' is the main verb, and 'for a picnic' is the complement, made up of a preposition and a noun phrase.

Thank u so much, it helped a lot :)