Silly question

I saw a show on Antarctica recently and it made me wonder something:
Let's say you decide to gather up the family and head to the south pole for a picnic, you are exactly at the south pole...what time is it?? ???
Wouldn't you be in every time zone in the world at the same time??
Or does the south pole have its own time zone??
Does the south pole change their clocks for daylight savings time??
Kind of silly I know, but it has really got me wondering how the heck you would tell time at the South pole.
Let's say you decide to gather up the family and head to the south pole for a picnic, you are exactly at the south pole...what time is it?? ???
Wouldn't you be in every time zone in the world at the same time??
Or does the south pole have its own time zone??
Does the south pole change their clocks for daylight savings time??
Kind of silly I know, but it has really got me wondering how the heck you would tell time at the South pole.