I know that at minus 70 degree Fahrenheit, we can grind PVC into
powder, e.g. using impact hammer.  The question is:  at what
temperatures can we grind PET (polyester) and ethylene-vinyl-acetate
(EVA) into powder.

This temperature called "glass temperature",Tg.

Tg (glass temperature) is the temperature at which plastic becomes
soft under normal circumstances.  I'm sure "soft" is not the proper
scientific term to describe this change of property, but to a layman
such as myself, plastic becomes soft at Tg.  During grinding, because
of friction and pressure, plastic becomes soft at a much lower
temperature.  For example the Tg of almost all plastic are higher than
room temperature, but if we grind them in room temperature, the
plastics will immediately become soft and gum up the machinery.  Our
experience with PVC is: we have to reduce the temperature of the
grinding chamber to negative 70 degrees F in order to successfully
grind PVC into powder.  My question is: what are the corresponding
temperatures for PET and EVA.

Below Tg a polymer becomes brittle and can therefore be ground to a
powder.
The Tg of PET is 342 K (69 oC)--it can be ground at room temperature. 
EVA is a copolymer of ethylene and vinyl acetate; the Tg will depend
on the vinyl acetate content.  EVA trade names include Elvax,
Escorene, and Ultrathene--the manufacturers should list vinyl acetate
content and/or Tg on their tech data sheets.
(Tg data is from Polymer Handbook, 2nd edition by Immergut and
Brandrup, eds.  The Tg listed for PVC is 354 K or 81 oC).