A thin, fine OR light drizzle would do. (talking generally about thin rain)
In a sense of lack of visibility, we could say "mist" (akin to fog).
As for you sentence, you could say "it´s drizzling now..." (as we say "it´s raining now, it´s snowing now) it conveys exactly what is happening now (the verb tense I mean).
But many people say "there is a drizzle now" which conveys "it drizzles now" and also "it have been drizzling for awhile and it drizzles now...". No one will sue you if you use this form, though.