Parents - Winston (father), Hazel (mother).
Emma Frost left home at an early age (Emma Frost #6), yet her family reappeared shortly after she was having trouble with the Boston mob (Emma Frost, volume 2). After Emma escaped the Boston mob and her family, not much has been known about her parents since.
We can assume her parents are dead, but we cannot provide evidence because not much has been mentioned about her parents.
Christian Frost (older brother) - Christian Frost was sent to a mental institution after Emma told their Dad that he was having a drug problem.
What is interesting, though, is that in Generation X #24 during a Christmas vacation, Emma told the girls a story of when she was taken away to a mental institute. Emma claimed the experience was horrible as she was lonely and the guards did horrible things to her. Then, Emma was later to control her telepathy to the point that she could control the guards' minds. She, of course, telepathically ordered the guards to release her from prison, and then she was able to set the mental institution on fire and set off on a new adventure.
Generation X #24
Writer: Scott Lobdell
Artist: Rick Leonardi w/ Mitch Byrd
Now, Generation X is an older comic, and since the Emma Frost series was released, this tale Emma told of her earlier days was obviously a lie (unless if you take it as a retcon, but a lie would make more sense). However, we can assume that Emma was most likely thinking of her brother during Generation X #24.
Current status of Christian Frost is unknown, however, we could assume he is dead due to the lie Emma told of Generation X #24....and that he has not appeared in Emma's life for quite some time.
Adrienne Frost (older sister) -
Generation X #75
Writer: Brian Wood
Artist: Ron Lim
In Generation X after Emma accepted Adrienne as headmistress in order to receive financial backup, Adrienne had an evil plan all along and planted bombs in the institute which killed the student Synch in the process.
Emma was, of course, infuriated by this and killed Adrienne with a gun. Status: Dead (and good riddance, too).
Cordelia Frost (young sister) - Cordelia Frost reappeared in Emma's life in the Generation X Annual '95 [read more. Cordelia needed help to track down a mutant named Mondo. Emma and the Generation X team were able to successfully locate Mondo, however, Emma quickly found out this was all a plan in order for Cordelia to become the new White Queen of the Hellfire Club. Emma was livid and told her younger sister to never come back to the school.
Emma's message was sent quite clearly to Cordelia as we have not seen her since.