No, you can definitely survive space for over a minute unless you try to hold your breath (and rupture) or there's radiation cooking you. Mostly you faint as your blood oxygen drops in 0 atmosphere, and you get membrane damage by the second from water turning to gas, which is the main thing reducing body temperature.
You cool very slowly, like being in a vacuum flask, so taking on any heat is deadly, even body temp in an unpowered space suit. The pressure is only the opposite effect of diving 10 meters, which can be felt but won't pop you. Normal medical expectations for oxygen deprivation apply, with heavy bruising plus possible frostbite around mucus membranes.