In fact, women were not even considered full citizens then since they did not possess the right to vote.
Like most things, this was up to the individual states. Like anything up to the individual states, it was all over the place depending on exactly where you were. For example, at the founding women in New Jersey could vote, presuming they owned 50 British pounds worth of wealth because the wealth requirement was the only requirement New Jersey had for who could vote. Ironically, the spread of Jacksonian democracy (aka universal male suffrage) actually cost women in New Jersey the right to vote in the 19th century.