What is an example of a very low temperature endothermic reaction?
Yes there are. In Vogels famous textbook on practical organic chemistry there is a section about the cooling effect of certain salt (mixture) solutions in water.


  If ice is temporarily not available, advantage may be taken of the
  cooling effect attending the solution of certain salts or salt
  mixtures in water. Thus a mixture produced by dissolving 1 part of
  NH4C1 and 1 part of NaNO3 in 1-2 parts of water causes a reduction in
  temperature from 10 to — 15 °C to — 20 °C; 3 parts of NH4C1 in 10
  parts of water from 13 to -15°C; 11 parts of Na2S2O3.5H2O in 10 parts
  of water from 11 to - 8 °C; and 3 parts of NH4NO3 in 5 parts of water
  from 13 to — 13°C


(Taken from Vogels 5th edition, p. 70)