It could be that there was not enough room in the Woodhouse carriage for all three men so they all three road horseback. Also Mr. Knightley, Mr. Weston and Mr. Churchill might want exercise and Mr. Elton who claims to be an old married man does not want to get the dirt of the road on him. Mr. Elton’s flowery compliments during the “he’s courting Harriet but really courting Emma” chapters have always suggested to me that he is a bit of a sissy. Worse yet Mr. Elton prefers the company of his wife to the comradery of the road. I favor the sissy explanation. (;D)