As regards hypo/hyperthermia - I agree with
@Jessey. There are lots of very sophisticated systems in place to regulate core temp as this is crucial for health, or even survival. By the time a horse is showing core temps outside normal ranges they are well beyond being uncomfortably warm or chilly to being dangerously hot or cold. Taking temps might be interesting as a research project or to reassure yourself - to assess whether a horse is being under or over rugged to the extent that they are at significant risk. But I would not use it as a guide to management as if they were really that hot or cold then something has gone drastically wrong.