Napoleonic Royal Horse Guards horse furniture

I am converting an Airfix 54mm 1815 Life Guard into a Royal Horse Guard
and have a couple of questions not answered in my main source
(Haythornthwaite's Uniforms of Waterloo).

* What was the horse furniture for this unit and how did it differ from
that for the Life Guards?

* Wasn't all British heavy cavalry horse furniture the same, and if so,
how come the Airfix Scots Grey has a completely different set up to the
Life Guard?

* What colour was the RHG cloak - heavy cavalry red? Grey? Dark blue?

Clues appreciated. Can't really stretch to buying an Osprey book for
one 54mm figure.