My grandmothers generation and my father in laws generation are ripe with traditional women, in their 70's and 80's with short hair.In later years, hair-length is not that important.
Did they have long hair when young?
Also, is there a reason they wear their hair short, and how short is it?
When I say short, I mean short: above the ears.
Think back to all the shows on television made popular in the 50's and 60's...all those traditional "moms" had short hair styles. It's a style, and the grannie generation still wears it.
I'd argue that the 60's and 70's brought back long hair. In fact, many claimed long hair was revolutionary and freeing. Heck, I know plenty of older babyboomer/ex-hippie generation women who still wear long hair. It may be grey but it's long. I'd say they are the antithesis of your traditional woman/long hair thesis.