Yes, in people and in horses, you need to distinguish. I am going to define supplements below as excluding actual pharmaceuticals which of course can also be given on an ongoing basis (Prascend, Regumate, NSAs, etc).
First there are vitamin mineral supplements, which provide known factors for optimal health. If a human is not eating a balanced diet they should be taking a basic complete VMS. Most horses also are not getting a balanced diet for various reasons so they too need a VMS or ration balancer. And salt.
Also there are components of basic diet like flax that can be seen as either a feed or a supplement.
Then there are medically effective
”‹supplements with research behind them. In any given case, you want your vet’s recommendation plus your own research to verify this. In this category I would put good probiotics and Yeasacc (which I’ve used successfully as needed) and the Thyroid supplement mentioned above (which I’m not personally familiar with).
”‹”‹”‹”‹A subset of this category is feed through joint supplements, which unfortunately don’t have strong research supporting their efficacy compared to either intramuscular or intra articular injections. This is one category of fairly pricey supplements that people will feed just in case it works, because there seem to be no ill effects
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Next down the list are vitamins and minerals fed in larger therapeutic rather than just maintenance doses, which have documented proof of efficacy. Here I would put extra copper and zinc for metabolic horses, extra vitamin E for some infectious diseases. Magnesium which can calm horses if their nervousness is due to magnesium deficiency. Etc.
Lower down the list are herbal or “natural” supplements that often have undisclosed or erratic levels of active ingredients, and can have rather extravagant claims. Very often, an inexpensive raw material (raspberry leaves, flax) is repackaged as an expensive brand name product. Here it really pays to do your homework.
So “supplement” is a very broad category. I am newly converted to taking my own VMS every day since starting it knocked out some leg cramps I was having over the summer and has made my exercise recovery time much faster. Clearly I was deficient in minerals!
So “why do people feed supplements” needs to be rephrased as “why do people feed supplement x?”
OP, do you have a specific supplement or supplement category that you are wondering about?