The German Army employed a series of branch colours to differentiate between soldiers in different trades and units. A detailed discussion of this can be found elsewhere on this site. In general, soldiers in any given battalion or regiment sized unit all wore the same colour. Before the expansion to divisional status, then, all soldiers of GD, be they pioneers, infantrymen, signallers, medics, etc. would have worn the white waffenfarbe of the infantry. These colours were used for the piping on shoulder boards (as well as the monogram on the shoulder strap, if in thread rather than metal) as well as piping on dress caps, dress trousers, etc.

 
Line infantry regiments were differentiated by the use of a number on the shoulder strap, in either waffenfarbe coloured embroidery, or in the form of a metal cypher in either yellow or white metal.  Grossdeutschland chose to use an intertwined "GD" device as its insignia.  For private soldiers and junior non-commissoned officers, the "GD" device was embroidered, senior NCOs wore white metal, and officers wore gold or yellow metal devices.  Actual examples of wartime shoulder straps are shown below.

After expansion to divisional status, all battalion and regimental sized units coming under Divisional headquarters wore their own branch colour, examples of shoulder straps worn are shown below. The only exception to standard German practice was the piping worn by the Grenadier and Füsilier Regiments - they retained the traditional infantry white even after the change in designation and role to Panzergrenadier/Füsilier, distinguishing between the two by coloured loops on the shoulder board.  Bear in mind that the boards shown below are the early war dark green style worn on the Feldbluse; field grey straps were more common as the war progressed, and some enlisted rank soldiers would have worn the black AFV uniform, with shoulder straps in matchng black wool.  The dark green are shown throughout below for convenience and consistency.

Michael Pruett, author of FIELD UNIFORMS OF GERMAN ARMY PANZER FORCES IN WORLD WAR TWO and co-author of FIELD UNIFORMS OF GERMANY'S PANZER ELITE passed on the following information regarding the uniforms of the Reconnaissance troops in the Motorized Infantry Division GD and later Panzergrenadierdivision (based on interviews with Knight's Cross bearer and divisional historian Helmuth Spaeter (2./Pz AA GD) and other unit veterans:

The 2. through the 5. Kompanien of Kradschützen-Batl. Grossdeutschland wore meadow green waffenfarbe from 1942 to 1943. The 1. (Panzerspähkompanie) wore golden yellow. In 1943 the Batl. was reformed/renamed as Panzeraufklärungs Abteilung "GD" and the entire unit converted to golden yellow waffenfarbe at that time which they wore until the end of the war.