I painted these guys a year or two before the films were released
Theoden (Donnington and Essex)
Eomer, Elfhelm, Grimbold and (dismounted) Eowyn (Donnington miniatures)
The Eorlingas (mainly Essex Miniatures)
I started painting the horses a mix of colours, as Tolkien doesn't actually say Riders only use white horses, only that they sent their black steeds to Mordor as a tithe, and a line that states that the front of Eomers eored "...roared like a breaker foaming to the shore..." but then had second thoughts and did the rest of the steeds white. The banner is of course The White Horse of Uffington which Tolkien would have known well and at the time of his writing the book I believe the general understanding was that the horse was of Saxon origin (we now know it to be Bronze age, but either way it is perfect art).
Again, there is no definite description of the shield device, as far as I remember, only a reference to some shields shining like the sun so I have done a mix of sunbursts and white horses.
Here they are appearing on the battlefield about to sweep into the orcs and carry all before them (What a great moment in the film, a real spine tingler)
and finally Theoden meets his end, but is avenged by his niece and a hobbit
(winged beast by Asgard, Witch King by Citadel, dead Snowmane and Theoden by Donnington)
I have enjoyed getting these old figures out again after several years and perusing the Rohirrim has put me in the mood to continue with my 1/72 early West Saxon army and their British opponents (almost finished the Saxons and just starting the Brits).