There are definitely some women who are afraid to admit that they support Hillary Clinton for fear of backlash from their conservative husbands, fathers, neighbors, etc. However, I think there are many more closet Trump voters, who are terrified to admit that they support him because of all the disdain for Trump among the majority of the country. Supporting Clinton is only seen as something to be ashamed of in a few specific circles, while supporting Trump is widely seen as shameful.
Yes, there are "closet" Hillary voters. In a "normal" election, conservative women have an easy choice: vote for the Republican who is pro-life and other conservative causes. To these voters, and their families and friends, Hillary and the democratic party are evil and to be fought at all costs. In this election, though, these women are faced with having to vote for Hillary or Trump, who has proven to many to be anti-women and minorities. To these women, if they choose to side with Hillary, they may do so in the "closet" for fear of being alienated by their surrounding conservative communities.
No, I don't think that women would be hiding the fact that they are voting for Hillary. Voting for her is definitely the safe answer, since the media is pushing her so much. Conversely, I believe that many women are closet voters for Trump since people attack them so severely.
No, I do not believe that there are "closet" women Hillary voters. Women that are voting for Hillary are often very proud and sure of their candidate. It seems very unlikely they would be embarrassed of their choice. I believe it is more likely there are "closet" women Trump voters. They may be afraid of the judgment and backlash from people about their decision to vote for Trump.