It certainly would seem like it, wouldn't it? The fact is, yes, but only in part. You are not a real cowboy unless you know how to ride a horse and rope from the saddle. Real cowboys should know how to saddle their own horses (the right way of course), gather up a lariat properly (and throw it just as well), and ride a green horse. You also have to be mindful of your behaviour and language around the ladies, show respect to others, and never hesitate to give someone a helping hand when need be.
So just because you can work with cattle doesn't automatically make you a cowboy. It makes you a cattleman of some sort, but not a cowboy.
Answer: Back in the days when cowboys were common, horses were the obvious choice if you wanted to get around without walking, so cowboys weren't named for what they rode(as everybody used horses), but for the animals they were working with - the cows. While it is true that cowboys roundup and work cattle there is also a place in a pecking order that the cowboy fits into. The Cattle Baron, The Cattleman and then the cowboy(who usually did all the work). This was what led to the illegal side of the picture which was the cattle rustler.
A cowboy, a cattle herder, a farmer or a shepard.
herding cattle
the cowboy needs cattle, food, horses and a laso
The Trail Boss
work, head cattle, bail hay, work on a prarrie open range, raise calf to sell for beef, and any other type of profitable live stock
In Spanish speaking parts of the US a cowboy or cattle driver
driving cattle to the plains for grazing
Vaqueros
A cowboy is an animal herder who tends cattle on cattle drives.
No, it's just laziness most of the time but some old timers 1900s guys used to do it to mean things like looking for work, have work, selling cattle, or buying cattle
A cow puncher is basically the same as a cowboy, a person that works with cattle. Before the 20th century the cowboy's job was herding, feeding, branding of cattle usually on a ranch or farm.