It's important to know what you can measure on a dressage saddle and what you cannot. You also need to know the correct way to measure things too.
Saddle Tree Size (width)
Many people often try to estimate a dressage saddle's tree width, but you cannot measure it. The saddle tree is buried inside the saddle. There is now way to measure it. Think of the saddle tree like a human skeleton. The bones have dimensions, but you cannot accurately measure them by looking at the outside of the human body because the skin and muscles are adding to the exterior measurements, much like the leather and flocking are adding to the exterior dimensions of a dressage saddle.
To get an accurate measurement of the dressage saddle tree, you need to get it from the manufacturer of the saddle. For example, most saddles are stamped with a serial number. The serial number gives you many pieces of information, including the tree size. Sometimes they tell you the exact measurement in inches or centimeters, and sometimes they just tell you size categories like narrow, normal, medium, wide, extra-wide, etc. You can also contact the saddle maker directly to learn about many saddle. Just provide them with a serial number and they will tell you the manufacture date, sizes of seat, flap, etc. They will also clue you into any additional features like upgrades in leather type.
Keep in mind that one saddle maker's definition of "medium" is not the same as another one's. You have to call a tack shop that deals in the brand you are interested in or do some research online to find this out. Of course, finding out the tree size is much easier when it's stamped in plain English such as "Medium."
Custom saddles tree sizes can be tricky. While the custom dressage saddle was originally built for someone and their horse, the saddle may not offer clues of the tree size in the serial number or otherwise. Custom saddles, such as Hennig, will not actually tell you a tree size at all because, in the case of Hennig dressage saddles, the tree is adjustable. Adjustable saddles like Hennig or Schleese are often readjusted when sold or when the rider changes horses or their horse develops.
Flap Length (height)
To measure the length of the flap length of a dressage or other English saddle, measure from the bottom of the stirrup bar to the bottom of the flap.
Seat Size (length)
For accurate seat measurement, measure the distance from the middle of the saddle maker's button to the highest point of the cantle. Keep in mind that you can measure this and it may not be dead on accurate with the saddle makers record. It may be slightly off by a half inch or so.
This 17.5 inch seat Albion Ultima SLK measures a touch over 17.5" from the middle of the button to the middle of the cantle.
The seat size is not an exact way to shop for saddles that fit the rider. It's just pretty close. The reason is that one brand of saddle that it 17.5 inches in the seat, will not often fit or feel like another maker. Some of this has to do with seat depth. Deeper seats are tighter fitting and shallower/flatter seats leave a lot more room for the rider to move around. More experienced dressage riders tend to prefer a deeper seat.
Like the tree size, the gullet size is not really measurable. The width of the gullet is effected by the amount and distribution of flocking as well as true size of saddle itself. People generally want to know how wide the gullet is in fingers. Everyone's fingers are different sizes, and if you try to photograph this, you cannot tell how big someone's hands really are anyway- especially when you factor in camera angle distortion.