No, they just transfer skills from one skill to another for the horse that does the rides. Beach rides do not influence BLUP or GP so are irrelevant to breeding.

Ok so if I understand correctly skill have no effect on the next generation. So if I do ride to increase jumping for 1000 generations the GP will be the same as if it was made to increase stamina for 1000 generations?
And if only blup and genetic potential matter that would mean I would get the same GP if I train 3 best and not the other / all 6?

Skills have no impact on breeding at all. Foal GP is determined by parents GP and BLUP as well as a small % variation built in so not all siblings are identical. You will get more variation in siblings born to lower GP parents than higher GP parents as the GP gain per generation is so much larger with lower GP horses.

BLUP is
- bolding the top 3 skills by completing forest (for dressage, gallop and jumping) and/or mountain (Stamina, speed and trot) rides until no more skill gain, completing the training bar and by entering competitions that use the top 3 skill areas until no further skills are gained
- winning 20 competitions
- horse being 10+years old

Only the top 3 skills are relevant to BLUP so there is no benefit to training the others if you are only interested in the foals GP gain. You may wish to train the other skills for competition purposes or to increase your general ranking though.

Foal skills are randomly assigned within certain % of the GP but can be increased by 1.5 times using Aphrodite's Tears. But this would only be useful if you wish to use the foal for competitions. If you only plan to breed from the foal then the increased skills of any individual horse do not have any impact on that horses offspring.

I hope that helps!

Yes, that was helpful, thank you!