Well Carbon Dioxide snow would be first, at a bit below -78.5 deg C.

Not so. CO2 would condense out of the atmosphere if the temperature fell
to a level at which the vapour pressure of CO2 equalled its partial pressure in
the atmosphere. At sea level this is 0.37 mb, and the temperature required is
-143°C. At, say 30,000 ft the partial pressure of CO2 would only be 0.12 mb
and the temperature required would be even lower, about -148°C. So no CO2
snow. To say that CO2 should condense out below -78.5°C is like saying that
water should condense out at all temperatures below 100°C, which of course it
doesn't, because its partial pressure is much less than one atmosphere, even in
the Persian Gulf.

Fortunately(?) for
the unfortunate few left on earth, Oxygen and Nitrogen would remain as
gases way down to the minus 200s.

At MSL pressure the boiling point of oxygen is -183°C and nitrogen -196°C
so the "minus 200s" is a bit optimistic. Hydrogen goes a lot lower, of course.
(Put that fag out). But we'd all be stiffs by then anyway.

Tudor Hughes, Warlingham, Surrey.