As title says

Because she didn't want to?

Because not every Muslim woman does. She obviously wore a hijab when going to Mosque or there was an auspicious event.

It's not a requirement, it's only in strict muslim countries where the mysoginists inflict it on women.

As above: Zainab was under no compulsion to wear the hijab when not at the mosque.

There's no explicit requirement in the Koran that women must wear a headscarf, and not all schools of Islamic thought deem it necessary (e.g. Turkey is a predominantly Muslim country but the hijab is banned in schools and universities.) A lot of women choose to wear it even if they're no pressure to do so, but I guess Zainab's not one of them?

I'm sure I remember Zainab wearing a scarf to mosque.

My understanding from a girl I know who married a Muslim is that the Koran only says that women should dress modestly (avoiding showing a lot of leg, cleavage etc) - it's cultural traditions that say whether this means wearing a hijab or a burqa or going without a scarf in everyday life.

Basically this! Their is a habit that one may associate a person culture to their religious belief and not accounting for their countries or culture tradition. While culture and religion have some overlaps which make them seem to say the same thing as their a number of things which are incorporated from ones faith.

For example their was a girl at my college that thought Muslims from Asia aren't Asains and only Muslims. She considered that only eastern Asians such as Chinese, Japanese, Korena ect. We're only true Asians. Similarly she was baffled by the concept of a Muslim living in India and a Hindu Bangladeshi... Because in her mind Muslim and some south Asains country traditions were the same. Similarly how a Asian Muslim might see all British traditions as Christian traditions...