Survivability is more a matter of heat transfer and less about the actual temperature. The temperature differential matters, but is only one factor and dwarfed by others.
Take space (in the shadows, so we are cold and not heated by the solar radiation), you'd asphyxiate well before you freeze to death. Initially most heat loss would be from your blood and other liquids (mostly water) boiling off, this would actually be most of the total heat loss (and decidedly fatal if you somehow didn't need oxygen). After that initial stage the only thermal losses would be blackbody radiation and it would take a total of around 8-12 hours for you to freeze solid (depend on body mass and other factors).
Even immersed in liquid nitrogen would take hours simply because of how slowly the internal heat would take to conduct though the body without the circulatory system to transport it.
At what point you'd die is a little complex, as the cellular processes slow down and eventually cease at lower temps, a quick search shows known instances of body temps as low as 18C being recovered from, so the lower limit is rather fuzzy. However even a drop of a few degrees of you core body temp leads to hypothermia that will quickly render you unable to remove yourself from the conditions and eventual death.