Regardless of discipline, your show coat should fit your body in a specific way for a polished look.
Shoulders
The shoulder seams of your show coat should line up with the edges of your shoulders. Narrow seams will make the coat fit too tight, restrict your range of motion, and impact the rest of the fit. Seams that are too wide will give you a boxy appearance and will likely bunch up while riding.
Sleeve Length
Though sleeve length does matter regarding the fit, this feature can be easily tailored so long as the shoulders and length of the coat are on point. The hem of your coat sleeves should reach about one inch past your wrist when your arms are hanging at your sides. Though that might seem long, once you lift your arms into riding position, the sleeve length looks and feels more appropriate.
Coat Length
Your coat length should fall slightly past your hips without bunching up around or beneath you while riding. If the hem bunches around your hips while seated, the coat is likely too long–try a "short" length if available. Likewise, if most of your seat or even your belt is visible while riding, your coat is likely too short–try a "long" length instead.
For hunt coats, you can use the bottom button as a length guide. The bottom button of a hunt coat should sit just around your belly button. If the coat button is higher than your belly button, the coat will be too short, and vice versa if the button is lower.
Overall Fit
The lapels of the coat should lie flat against your chest without any bunching or pulling at the buttons. Likewise, the fabric across your back should lie flat without wrinkling or bunching. The front should button easily without pulling or stretching. Try on your coat with a vest if you wear one for your equestrian discipline to make sure everything fits comfortably.