They actually sell computer programs for just this thing, you can look into that if you would like to go that route.
I myself like paper copies of things like this, as I'm lets say old school...not old, just old school
Each of the horses on my property have an individual file ( I use a 3 inch binder so pages can be added or taken out as needed)...in this file I have the following....
A recent picture of them
Thier name, DOB, breed, sire and dam (if known)
Colors and markings etc
In case of a boarder horse (name of boarder, contact info, and emergency contact info
I then have a page(s) set aside in the binder for farrier visits, vet visits, training, feed and feed changes.
I just add my notes in the binder as needed under the appropriate page with the date, what was done, by whom, etc.
It works great that way if I need to know any particular info on that horse, I grab the file flip to page I need a look back to find the info Im looking for.