Dishwashing detergent is designed to cut through grease particularly well, so strips the natural oils from a horse's skin/coat particularly well. Presume it would effect the protective coating of fats/oils on the surface of the hooves in the same way. Not sure it's any worse than shampoo in that way tho, or too bad if used very occasionally - eg before a big show. Also know that dogs' skin is different to ours - think lower pH or some such to ours, so even regular human shampoo is too harsh for dogs. Not sure if horses are similar in that way.
Vegetable oil can be OK, if a horse needs more condition & it does also tend to enhance coat shine, but adding fats can also be harmful if unneeded, too much, type dependent - eg. high omega 6 so imbalances omega 3's etc - and should be added very gradually & fed little & often in VERY small amounts, because a horse's digestive system is not designed for them, so digestive enzymes need to be produced & maintained to deal with them.
Electrolyte supplementation can sometimes be necessary, but generally only for exceptionally hard working, big sweating horses - eg endurance horses during/after a big race. It can be harmful if given when not needed or given regularly.
So... not at all saying what Tianimalz does wrong or bad at all, but we don't know the details or how/why for a start, and you need to understand the reasons & effects before just 'trying' something someone says. Could do a whole spiel on when it may not be a good move to use what I suggested too. By all means, listen to & consider all suggestions & opinions, but don't just blindly follow them without knowledge.
BTW Joe, great point!
I am constantly surprised by people who think 'natural' is the same as good/right/safe, etc. When people say something like 'it's natural so it's obviously fine' my line is "yeah, that's why it's really a myth that arsenic & toadstools can kill you" ... on that note, that's why the lable 'barefoot' or 'natural' hoof care grates on me a bit, because while I think that generally we can do far better for our horses than conventional shoes, bare feet may be natural, but...