I don't think that "open-heartedness is a virtue Anne doesn't possess". To whom, really, can she confide or express anything at all?

I see her reserve not so much as an ingrained part of her character, but more as a matter of necessity for her. She does have bursts of feelings, and although she is well able to hold her tongue, she struggles with the feelings inside her--again more because she has no one to whom she could relate any of them for many years.