You seem to be confused a shabraque is NOT a saddle cloth and the broad sense as we know it today, it was more of a saddle covering, and it is absolutly not artistic licence by period artists!
A majority of napoleonic military saddles were mostly all Hungarian style except for the officers who preferred German hunters (more comfortable) hence the shabraque was sometimes underneath.
Hungarian saddles can be adjusted to fit any rider and have a High Gullet so they will fit any horse (high of flat withered)and have the added advantage of adjustable side bars so as the horse lost conditioning due to campaigning the saddle could be adjusted to refit the horse. also the hungarian saddle had platted horsehair (the best as it breathes)felt or sheepskin padding fitted onto the sidebars.
The padding sits directly onto the horse withers and back, hence the Hungarian saddle doesn't need a saddlecloth, only if the horse had lost a lot of condition would one have been used.
Saddlecloths were used by the British as their trees were not adjustable (1778 model) and they used a girth and circ single arrangement, although they were mostly replaced by the 1805 ('Light Horse Saddle', designed by Sir Wiliam Erskine) model based on the german dragoon style with longer flaps.
the sheepskin shrabraque was for the benefit of the rider not the horse making the laced harness more comfortable (but horrible in wet weather!)
It is described well here
link
and the Hungarian saddle here
link
german hunter and hungarian together
french (hungarian style) hussar saddle
link
german cuirassier saddle 1786 model, however the tree is hungarian,this is more commonly known as the dragoon saddle, note the side skirts or leather flaps, and also note no saddlecloth, primarily used by heavy cavalry and you guessed it dragoons.
images.nypl.org/?id=1506227&t=w
a good read if you have time, although it is written some 100 years later
Horses, saddles and bridles capt W H Carter
link
and reproduction saddles (english)
link
my two cents
cheers
matt