Thanks Dibble. Based on your comments, I've done a bit more research (references 1 and 2) and found the following:
1: From 1768, the cavalry had housings and holster caps that seem generally to have been in the facing colour with edging in the lace colour. There were exceptions in the heavy cavalry regiments some of which had red housings (1st Dragoon Guards, 1st Dragoons and 4th Dragoons). Housings were not usually taken on campaign. White goatskin (troopers) and black bearskin (officers?) saddlecloths were also used
2: A warrant was issued on 27th July 1796 abolishing horse housings and holster caps for troopers for all the cavalry. Officers could continue to use them for a while longer and there is a paintings from 1808 of an officer of the 4th Dragoons with them. This warrant would explain Dibble's comment about not seeing pictures of them. It's unlikely that the officer's housings were used on campaign. Either a plain saddle or a grey blanket was used in the field.
3: The first Hussars appeared in 1805 and they adopted shabraques. There are paintings of officers with them in sometimes in the old style with a field in the facing colour and edging in the lace colour. Later pictures show troopers on campaign with blue edged in white or red (15th).
4: Shabraques seem to have been adopted by the rest of the cavalry (along with sheepskins) with the 1812 dress uniforms. Light Dragoons had blue with edging in the colour of their regiment's lace, Hussars were as above and Heavy cavalry had the facing colour with lace colour edging. The 4th Dragoons seem to have stuck with a red field. These were not taken on campaign- again agrey blanket to protect the horse was used.
There is a later note from the 1820's saying that housings had not been issued to the heavy cavalry.
In summary, other than for Hussars, it seems that shabraques were not used from 1799 to 1812 and certainly not on campaign. They were only used in full dress with the 1812 uniform.
References
1: Barthorp, British Cavalry Uniforms since 1660, pages 48 to 77
2: Journal of the Society of Army Historical Research Articles by the Reverend P. Sumner in particular No 55, page 138