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For the skills to be higher than the GP, the horse needs inborn skills (born with skills), which comes from the parents both having positive blup, preferably 100, when bred. Aphrodites Tears on the mare will increase that amount.

If the skills ended up less than GP, then you likely trained the horse when it was less than 100% health. Training at less than 100 health will incur a skill penalty.
Bonuses do not add skills. They only offer a bonus for competition.

If you have further up information to provide, or if your whole question won't fit in the character limits, then it's best to ask your question in the game help forum.