My mom told me it’s not proper to have long hair when a woman gets older.
I would disagree with your mother. Older women can look great with longer hair - even if it turns gray or white. I have this conversation with my wife from time to time. We are going into our mid 50s and I still insist on her keeping her hair long. I find short hair on women so unattractive.
Below is an older woman whose hair turned white. Not my wife but the hairstyle is similar.