Several of the horses gotten during the tutorial cannot be sold, given away, or killed at all.
An account requires a minimum number of horses on it in order to be able to function. Certain gameplay mechanics become inaccessible if your number of horses drops too low. The tutorial horses are made unsellable and unkillable to ensure your account always has the bare minimum number of horses.

work the horses and collect and SAVE the droppings. you are going to need LOTS of droppings for the beginner objectives. Don't sell them til you get the objectives to sell them

Besides using them to collect and save droppings, enter comps with them too. They won't earn lots of equus, but what they do earn will add up and is fairly easy money on this game. They'll also find aging points from time to time, which will help your game.