Yearlings do not show any information related to stats. This includes both traits and hidden stats. They also do not have the option to buy full genotypes. There is a skill you can earn which will allow you to purchase genetic ratings for them, but otherwise none of this information can be shown or purchased. Those who have purchased stablewide Hidden Genes will still see those. You CAN also still purchase genetic merit evaluations for them.
Yearling training is called groundwork. By doing groundwork, you are sensitizing and desensitizing your yearlings and preparing them to begin under saddle training when they turn two. There are two key factors two yearling training. One, they will gain stats much like older horses do when trained, but they will only gain stats in rating and versatility. Realistically, you aren't teaching a yearling skills like speed or breaking from a gate yet, but they are learning how to be respectful and obedient to their handler (rating) and adapt to changing situations (versatility). Secondly, they will gain courage and consistency. The rate of gain in these stats is directly related to their Temperament genes, so horses with a better disposition will improve more quickly in these areas.
There is a special section on pages for yearlings called Yearling Assessments. This will show a rating in stars, from 1-10. Yearling assessments are based upon what you would look for if you were going out to actually purchase or evaluate a yearling. This rating reflects upon overall conformation and physical development, attitude and disposition, and an anticipated aptitude for racing. As your yearling trains and grows, this rating can and should improve throughout the year. However, bear in mind that this rating is based upon what you could realistically judge by looking at a yearling - it is not all-encompassing or definitive in nature.