Using 'nose around' can imply invading someone's privacy or space without permission. He got in trouble for nosing around his sister's diary.
Pro Tip 2/3
Curiosity Driven
It often suggests looking for information driven by curiosity, not necessarily with a bad intention. They nosed around the old house, fascinated by its history.
Pro Tip 3/3
Negative Connotation
'Nose around' can carry a negative connotation, suggesting meddling in affairs not one's own. Don't nose around in matters that don't concern you.