I use my horses' names to give a hint to their lineage - for example Seabird x Hot Take has a foal named Hotwings or something similar 😂

Inbreeding will not affect your horses aside from value to yourself or to other players also looking for "clean lined" horses. I usually only check the first page of lineage and if that's clean, it's good enough for me. 

I've seen a lot of players use symbols in front of or after their horses' names to symbolize a sire or dam, too - maybe that would help you!

I created a tag (they're in Estate > Manage) for some of my more heavily used foundation horses, and apply it to their offspring. Then each foal gets its parents' tags. This at least means my own branded horses aren't inbred to branded sires.

Of course this won't help for any external breedings, but you have to decide how many generations you care about, and just manually check.

If your idea is to never have a single horse appear more than once in a horse's lineage, and if we consider that foundation is generation 1, you will need 2^(current generation - 1) foundation horses. For example, for generation 9 you'll need 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 foundation horses, 512 for generation 10, 1024 for generation 11, etc... Are you sure this will be sustainable?

That's why many people choose to not have 'visible' inbreeding, meaning no inbreeding that you can see from glancing at a horse's lineage in its profile. Personally, I just check the visible lineage of pairs I have in mind before breeding the 'breed now' button.

Thankyou everyone! I was thinking that even a third generation back would affect my horses genes and such but I seethat I was worried nothing! Once again thankyou!!