I smell trouble brewing.  Let's figure this out before an edit war starts.  I see a few issues here in dispute: 
1) Cold-blooded=stockier draft type vs. cold-blooded=origin in cold climates.  I had learned it as the draft-type definition, but I have seen both definitions in use.  I don't necessarily think they are mutually exclusive.  While I think that the geographical terminology likely defined the core original breeds, with years of interbreeding this becomes messy.  So many breeds have differing degrees of both types.  For example, Warmbloods are not the only mixtures of European and Arabian blood.  Wouldn't this strict definition mean that Quarter Horses would be a type of warmblood? My feeling is that we can say something like: "The hot-blooded/cold-blooded terminology originally related to the geographical origin of the breed, but now has come to refer to the overall character of the horse or pony."

2) Ponies (most if not all) are cold-blooded because they originated in cold climates vs. some ponies are cold-blooded because they are draft-type.  Again, I think we can finesse this without saying that one is right or wrong.  I personally think that most ponies are draft-type, and so could be considered cold-blooded, with certain hot-blooded exceptions like the [Hackney pony].  Although, really, come to think of it, lots of ponies are more like little warmbloods...

3) Ponies were not used for 'draft' work in general because they were too small.  As I understand it, some pony breeds flourished at times because they were useful as draft horses in the mines.  For example: "when the coal mining industry became extensively developed in Britain in the 1800’s, Shetlands were imported in great numbers to haul coal cars in the 'pits'." (From "Shetland Pony")

Just my two cents...