My Reds have greatcoats mixed in with those in blouses, but my Whites don't have greatcoats. Instant recognition at a distance. This includes cavalry. It helps that Peter Pig have so many troop types that you have dozens of poses to chose from.
You could do it with caps instead - White troops only have one type of cap or fur hat, but Reds have a mix of caps and fur hats. Fur hats are quite easy to sculpt, so you don't need to head swaps.
You could also line all your Whites up in straight lines across the base, and have the Reds more higgeldy-piggeldy.