Platies are generally tropical fish and i wouldnt sell thm to an unheated tank. The variatus platies are slightly different, they tolerate a lower temperature and will happily live in 18-22 deg C.
The trouble is, can you pick out which is a variatus platy and which is just a variatus coloured platy? I cant... therefor i wouldnt want to risk it.
Like a lot of species, platies will tolerate low temperatures, but then again so do humans, doesnt means its what they need or that its doing them any good. I hate being cold, i struggle to do anything if im not warm enough, i eat less and do less when im cold (im sure im cold blooded!)
EDIT:
Most platies and livebearers bred for the pet trade arent like their wild type 'ancestors'. The are mainly bred in hot countries like Singapore and Sri Lanka and places where even kpt unheated... its still Tropical temperatures! So you are suggesting to keep fish that have been bred in tropical temperatures for numerous generations.... in cold water, in a much colder country...