I would second the notion that a good horse has a good attitude, and is willing and responsive. The "easy-to-catch" part comes in mighty handy, also, because if a horse is hard to catch it is often much less frustrating to just catch a friendlier one to get the job done. It might not be very "cowboy," but using a piece or two of cake (protein cubes) keeps them more gentle and easy to catch.
Some things I dislike immensely in a horse, to the point of not keeping them around, are: stumbling, rearing up, and bucking after they've been ridden for half a day. It is understandable and acceptable if a horse is a little cold-backed early in the morning, but after they are good and warmed up and still want to buck, they probably don't need to stay on the ranch. Endurance is also something I greatly admire in a horse. It is no fun riding something that you have to pedal to get across the pastures. Endurance is important enough to me, that I rate a willing ground-covering traveler higher than one with super-dooper power steering. We do a lot of wintertime riding and I always wear lace-up high-topped overshoes over my Wilson boots. The spurs are left in the barn in these conditions, so I don't like to ride horses that need to be ridden with spurs. My lifetime of observation has concluded that a good cowboy can accomplish more with a poor horse than can a poor cowboy on a really good horse.
