Horses can be warm, hot or cold blooded it matters where they live. They are mammals. So they do have vertebras. I will describe what hot and cold-blooded are.
1) Hot Blooded Horses
The hot-blooded specialist adaptations to life in a hot and dry climate were physical and psychological. They produced a fine-skinned, narrow-bodied horse that is sensitive and quick to react. Commonly called ''blood horses" these types evolved in hot regions. Needing to lose body heat easily, they have fine coats and thin skins with blood vessels near the surface to allow heat to radiate out though the skin. The fine coat mane and tail hair help with this. Even the winter coats of such animals are not long and heavy. The head of the hot-blooded type is short and relatively narrow with large nostrils, allowing hot air to be breathed out. The ears, which hold plenty of blood, are large to release heat, and their necks and bodies are often long and oval shaped; again to help with heat loss in comparison to a more rounded body.

2) Cold Blooded Horses
These horses include the British native ponies and heavy horse breeds. The main concern of the cold blood types is retaining heat, so these have longer air passages to warm cold air, which could otherwise cool lungs and heart. The neck of these horses is short and round. Their body is round with short legs. Their tails lie close to the body and the skin sweats less freely. Coats are thicker and longer, creating a greater overlap to retain an insulating warm air layer next to the skin. Mane and tail hair is long, thick and wiry for added protection. Most cold bloods have super efficient metabolisms and retain condition with relatively little food, which is not good for them.

3) Conclusion
California has a mild
and warm climate, that is, it is not very cold in winter and not too hot
in summer. For that reason, if I were to get a horse, I would get a warm-blooded.
-fb