Here in the US - it is grey if you are the owner and or owner/driver. Black if you are driving someone else’s horse(s) or you are the employee coachman. However, I have seen grey top hats on gentlemen who are driving a team that is not their own, but are on a coach that is theirs.
A top hat is acceptable for a formal or sporting vehicle. Top hats are not supposed to be worn in either family or informal vehicles.
If the driver is the owner, and is wearing a top hat (grey, of course), then his staff should also be wearing top hats (staff is always black, NEVER EVER grey). On vehicles other than coaches the staff can be excused to wear a black velvet hunt cap. On a coach, however, they should be in black top hats if the driver is in a top hat.
Correct: Owner/driver in grey, staff in black
http://www.flickr.com/photos/martinavannelli/403881815/in/set-72157594233256500/
Correct: Lady whip, gentleman friend in black top hat
http://www.flickr.com/photos/martinavannelli/403881807/in/set-72157594233256500/
Correct for driver and staff. Gentlemen in grey - questionable as to why unless they are fellow drivers (I think I recognize one and he is a noted whip) - or that is the only color hat they had!
http://www.flickr.com/photos/martinavannelli/403871452/in/set-72157594233256500/