Hi @ZuzuMyLittleGingersnap happy to. It's thought that there's two main mechanisms through which placebo effect is observed in animals. One is because the handler administers the medicine, feels they are doing something to help, calms down themselves. The dog/horse is very attuned to it's handler and therefore calms down. Just like in humans, pain is verry linked to emotions; in dogs particularly. Everyone knows dogs are very stoic. Our mood effects that.
The other mechanism is that the handler is often the one reporting the symptoms. The handler believes symptoms have reduced because they have done something so they report fewer/less even if the animal feels that same.
These two can of course work together. Animal feels less, handler reports EVEN less.
Then there are other effects (not the placebo effect) but they work in the same sort of way. One is reversion (or regression) to the mean. If you're trying Rescue Remedy chances are your dog/horse is feeling worse than it ever has, just really terrible and you are desperate. You'll try anything. You give the dog/horse the drops, the dog/horse gets better because it's typical state is better. It reverts to it's normal state. It's why things like acupuncture work on humans. "I'll try anything" means you are at your worst. Your worst isn't typical. A lot of alternative therapies even say, "you might feel worse before you feel better" so even a slight slump is seen as 'working'.
There's also white coat effects (for good or bad) which are confounding variables. My dog loves the vet so if someone in the vet's gave him a drop of something, he's feel better. Yours might hate the vet.
Well-designed experiments can show that none of this is the homeopathy/Rescue Remedy or whatever doing something. But they ARE useful. Around 80% of the painkilling effect of morphine is placebo. Harnessing that is GOOD. People think calling something placebo means we're scoffing. But actually if charlatans weren't profiting, we wouldn't be. If it was used for good, what's the issue.
I get acupuncture. I know it's probably bollocks but being ministered to, cared about, talking about my symptoms, having someone sit with me and care, not something one can get on the NHS currently. I spent an hour with a calm-talking, caring, sympathetic, very hot, seriously looks like a model acupuncturist and I feel better. I'm also relaxed in a chair, under a blanket, nothing to do for an hour. It's great.