Show jackets, as the name suggests, are designed to be worn by horse riders at shows or competitions. They are not usually worn in everyday riding and are worn mainly in the equestrian disciplines of dressage, show jumping or showing.
As show jackets are specifically designed for wear in the saddle they are created with a certain amount of stretch so they will not hinder your ability to ride or restrict your movement as long as they are correctly fitted. However if the jacket is too small, you may find that it restricts your movement, particularly in your arms. It may also sit uncomfortably tight around your body and ride up as you ride. Alternatively the jacket may sag and look less than flattering if it is too large.