Horse breeds can adapt to whatever climate they live in as long as they have some form of shelter from wind, rain, and blazing sunshine. Individual horses themselves may have some type of medical history that would precluded them from adaptation to climate. The horse's comfort zone is between 15 degrees and 75 degrees farenheit. Horses that are kept in barns and stalls and not allowed to grow winter coats cannot take the cold like a horse that does have it's natural shaggy winter coat. Thoroughbreds and Arabians (hot bloods) do quite well living in cold climates just as well as warm. Draft horses (cold bloods) can live in very warm climates. Moving a horse from one climate to another takes an adjustment period for them to get in sync with nature.
Yes warm bloods
There are various different kinds of horses. And each of this kind has different stamina for survival in relation to temperature and weather. In general they can be divided into hot blooded horses who are from hot weather zone, cold blooded horses who are from the colder regions and warm blooded horses who are from moderate and tropical regions. For more information on horses see the link below: