"T" is for temperature, "P" is for pulse, and "R" for respiratory rate. Practice taking these when your horse is at rest so you can determine what is normal for him.
Temperature: A horse's temperature is most accurately taken using a rectal thermometer. It should be coated with a lubricant before it is gently inserted and materials such as mineral oil, petroleum jelly, liquid soap, or vegetable oil have been used successfully. Always hold onto the end of the thermometer while it is in place (or have a string tied onto it), as you stand to the side of the horse (not directly behind him). The horse should be appropriately restrained during this procedure, preferably by having someone at the horse's head. Keep in mind that this procedure is not recommended if there is doubt that the horse will tolerate it.
Season and temperature can slightly influence the horse's temperature. And immediately post-exercise, its temperature may be slightly elevated above what it would be at rest.
Pulse: The horse's pulse rate can be taken most easily using the superficial artery that runs along your horse's jawbone under his cheek. It will feel cord-like and is movable under the skin. Press the artery against the inside of his jaw bone using slightly curved fingers, and you will be able to feel it pulsating. Count the pulsations occurring within a minute. Pulse rate is also influenced by several factors such as exercise, stress and excitement, physical condition and environmental temperature. Younger animals tend to have higher pulse (heart) rates and certain breeds such as Draft breeds may be lower.
If you have a stethoscope, you can also listen to his heart (low down on the left side of the chest wall). Count and record the "beats per minute" or bpm.
Respirations: The respiratory rate (numbers of breaths per minute) is taken by observing your horse at rest and counting the numbers of inhalations (exhalations) in a minute. You can observe his chest move in and out. With a stethoscope, you can listen over his trachea (windpipe) and count respirations.
Temperature 100°F (+/-1°F) OR 37.8°C (+/-0.5°C)
Pulse 28-40 bpm
Respiration 10-14 breaths/minute
*Ref.: The Merck Veterinary Manual, 9th ed.