Me and my friend were arguing, how long is it possible to survive
under a temperature of -90c/-130f, in normal (room-temperature)
clothing. The temperature of -89c was recorded at the Russian Vostok
weather station, July 21, 1983. Even considering there will be no
wind, I argued that it is impossible to survive more than a minute,
you will have better chances survivng naked in the
ice water (ironically). However, is it really possible to tell? What
will going to happen, if someone was exposed to such a temperature in
normal clothing?

Living in fairbanks alaska, I've frequently been exposed to -40
frequently and even -50 every now and then as I walk to and from
class. Since the distance is reletively short, at least once a week I
do this in normal indoor style clothing. Though it is very cold, the
only time I ever felt in danger from the cold is when it is windy,
which is almost never here. -90 of course would be even more extreme,
but this should give you some idea that you can last longer than you
might think. Definitely it would be better than being in icy water
because water is an excellent conductor of heat, standing non humid
air even at -50 will not draw heat away from you as rapidly as icy
water.

by the way i didnt see the remark -90C, i thought it was -90f. the
-40f i referred to is actually identical to -40c.

According to this site:

http://www.coolantarctica.com/Antarctica%20fact%20file/science/cold_humans.htm

exposed human flesh will actually freeze (i.e. get frostbitten) within
seconds rather than minutes if exposed to an equivalent (i.e. with
windchill) temperature of -66C - which is about as cold as it really
gets on our planet, most of the time.  Whilst no-one has actually
frozen a human being to a lower temperature than that (obviously) I
think it is safe to assume that the effect worsens as the temperature
drops further.

Indoor clothing offers little protection from the cold and leaves
extremities (including the head, importantly) fully exposed.

We also need to consider "shock".  The physical shock to the human
body from being exposed suddenly to such cold would be enormous - and
may well induce circulatory problems (heart problems) or effective
shutdown of the brain.  Without getting grizzly, this would be very
bad!

Now for some physics.  Consider the energy radiating from a warm body.
 This depends linearly on the relative temperature of the warm body
and its colder surroundings.  The bigger the difference, the faster
the energy flows.  Flow of energy is known as "Power" - an amount of
energy over time - i.e. Power (P) equals energy (E) divided by time
(t) (P=E/t).  We know all this because a cup of coffee gets cold
quicker in the fridge than on the kitchen worktop.

So if a certain amount of energy flows out over time, then that energy
must be replaced in order to maintain the temperature of the body, and
thus the key question is: how much energy can the human body produce
in a given time?  Or more accurately, what is the Power output of the
human body?  At rest, the human body generates 400 watts, which is not
a lot (about the same as a desktop computer).  No-one seems to know
what the maximum we can produce is but we should note that as the
heart-rate slows down (which happens in extreme cold) the power output
of the body will necessarily decrease.

An aside here is to mention that this is the point of shivering -
because it causes the muscles to work, the power output of the body
rises, and thus so does the heat generated by it (hence you get hot
when excersising).

So to your question, "What will going to happen...?".  This is what:

1.  The shock would initially cause the heart rate to dramatically
decrease.  Breathing would shorten, and perception would decrease as
blood flow to the head reduces.

2.  The intense cold would be felt immediately at the extremities,
including the fingers and head (I am assuming they are wearing shoes).
 Blood flow to these regions would initially increase, and then
dramatically decrease leaving the flesh white (frostnip).  Finally,
the tissue at these extremities would freeze (frostbite).

3.  The core body temperature would decrease quickly due to the heat
radiated through the clothing.  Once the temperature went below about
30-33 degrees, the person would become unconscious.  As the core
temperature decreased to anywhere between 20 and 28 degrees the person
would die because the heart would stop pumping.

The only question is, (and I don't have the answer):

Would the person's brain freeze first (with the other extremities) or
would it be the reduction in core temperature that killed them?

I expect probably the core temperature would be the killer, since the
brain has a big supply of warm blood straight from the heart.  In
which case they may have a little more than a minute.  However, to
defrost their extremities successfully would be near impossible so
they wouldn't have much of a life after exposure to a minute of this,
since some amphutation of the frostbitten parts would be necessary.

All in all, a very nasty prospect for whomever was holding that thermometer!

Canters