The 'tassels' are in fact olivets which are the vestiges of the former "fasteners" for the frock coat. In the original practice the olivet would be fastened with a toggle.
Doeskin in this context is actually a woven fabric made from 100% Merino wool, tightly milled, in a twill weave, with a face finish. The term ‘Doeskin’ originated from the similar appearance and feel of the fabric to the skin of a female deer.
The whole ensemble is carried through from the service dress of the heavy cavalry regiments the were amalgamated in1969 to form RHG/D and originated with the Hussars who morphed into Dragoon Guards.