The first downside is that she cannot hope to have eternal marriage unless her husband calls her at the resurrection. If he fails to do so, she will be resurrected, but not as his wife, which can potentially keep her from becoming a goddess.
Do the women, when they pray, remember their husbands?... Do you uphold your husband before God as your lord? "What!—my husband to be my lord?" I ask, Can you get into the celestial kingdom without him? Have any of you been there? You will remember that you never got into the celestial kingdom [during the temple ceremony] without the aid of your husband. If you did, it was because your husband was away, and some one had to act proxy for him. No woman will get into the celestial kingdom, except her husband receives her, if she is worthy to have a husband; and if not, somebody will receive her as a servant. (Journal of Discourses, vol. 5, p. 291)
Women who go through the temple receive a name. The only person she is to tell this to is her husband. A husband does not have to tell his wife his name. This is because God will call a man into the Celestial Kingdom, but a man--not God--calls his wife there. These names are usually from the Bible, which means that many women probably bear identical names. It leaves one to wonder how they'll know who is who in the resurrection, with all those "Rachels" and "Eves" waiting to hear their husbands call them.
Then comes the role of a woman in eternity. It is much like the role of a woman on earth: to bear children. On earth, it is for the purpose of giving bodies to as many spirits possible. In many cases, there are women and families--especially early on or in fundamentalist sects--that prohibit or strongly discourage birth control, and see anything sexual that is not for reproduction as impure, even between a man and wife. Although this has relaxed a little in the mainstream church, there is still a push to have as many children as possible and to start young. Masturbation is still seen as a sin, and while sex is allowed for pleasure even when a woman isn't fertile in the mainstream church, I have had the impression before, both as a member and as an ex-member, that anything for pleasure outside of sex itself is somewhat discouraged. I don't know if leadership are told to actively discourage this if they learn of it, however, or if they used to but no longer have to.
In eternity, the purpose of bearing children is to create spirits to continue the race of gods. Presumably, these spirits will repeat the same pattern we are supposedly repeating--they will go to earth, sin will come to test them, they will have to prove themselves worthy and faithful, there will have to be a savior to justify those who are worthy and faithful, and then the select few who meet the rigid requirements will be exalted to godhood eventually as well. Considering that billions upon billions of people have lived on this earth, and more are being born every day, the amount of spirit children a woman has to have is staggering. Even assuming gestation for a spirit is significantly shorter than women must deal with on earth, and that birth is not nearly so arduous a process, it would still take a long time for even multiple women to bear one man that many children, and the idea is simply exhausting.
This, of course, gave rise to polygamy. Polygamy was not, as most Mormons are led to believe today, just to take care of women whose husbands had died. Marriage is not necessary to do that, anyways. The church could have made other arrangements to care for the widows and orphans. There's also no indication in early membership records that there was a significantly larger proportion of women than men due to the persecutions. In reality, polygamy was to fulfill the dual purposes of a family creating bodies for as many spirits as possible (and fundamentalist sects believe more children means more guarantee of exaltation and great eternal rewards), and then given an exalted man--a god--as many spirit children as possible.
Polygamy can still be seen in the mainstream church, just in a "legal" way--since polygamy being illegal is what made them stop practicing actively in the first place (the Manifesto was not a "revelation" and wasn't God commanding it to be stopped forever; go read it yourself). Now, if a Mormon man dies and his wife remarries later on, she has to chose which husband she wishes to be sealed to, she can't be sealed to both. On the other hand, if a Mormon woman dies, and her husband remarries later on, he can be sealed to both, and both will be his wives if he becomes a god. Although I do not know for sure, I would not be surprised if women who are unmarried when they die are sealed by proxy to worthy Mormon men. As far as I'm aware, there is also a belief that if a woman is worthy and is either a Mormon with an unworthy husband or accepts Mormonism after death and her husband does not, she can still be given to a worthy Mormon man. Whether or not this is official taught, I know there are members who believe it, which makes sense in light of all their other beliefs on marriage and exaltation.
To add insult to injury, if our own "Heavenly Mother" that the Mormons believe in is any example, a goddess won't even be acknowledged by most of her children, and the few who do know she exists won't worship her, don't pray to her, and will barely talk about her. The Mormons say things like, this is to protect her from insults and blasphemy, but I would think a goddess could handle herself. No, in reality, this is because our heavenly mother--or mothers--are inferior to their husband and less powerful than him because of a single thing: the priesthood. He is the priesthood head in their family, so he is in charge, and therefore he is the one who is involved with his earthly children and their world; the women do not have the power to do anything in their childrens' mortal lives. It is his earth, and she is just one of the necessary components in his eternal exaltation.
Women, I have to ask you: does this sound like exaltation...or damnation?