In Explore, it told me that my 100% groundwork trained horse still needs more groundwork. She also often wasn't feeling very brave (she's Premium bravery). Is it purely random chance what it tells you, or does the result vary with training and bravery rating (and I've just been very unlucky)?

You get those same generic messages regardless of how much training the horse has.

So does that mean I can ignore both bravery rating and groundwork training, because they have no effect?

No, training in a roundpen makes your horse less spooky and a higher rated horse is less likely to spook in the first place. The messages just stay the same because they're generic and don't distinguish between the horses.

Thanks for your replies, they were helpful.