A cowboy a Saurus Scar Veteran or Oldblood mounted on a Cold One and usually deployed by itself without joining a unit. More commonly a Scar Vet than an Old One. There are MANY variations in builds but the most common thing you see in 8th ed Lizardmen lists is a Scar Veteran with the Armor of Destiny and a Great Weapon. That gives you a 1+ armor save, 4+ Ward save that hits at Strength 7 and doesn't cost a lot of points.
Also these guys are extremely flexible. They can take on most characters, monsters, monstrous cavalry and if you're not afraid of combat resolution they can hold up huge blocks of units. Just watch out for S6
They sound mean aprly suited name cant wait to try it finally finished my first unit as of 2 minutes ago.
Either is good, although I usually run them with other cold ones. You should check out our exhaustive 8th edition strategy guide on cold ones and Saurus hero's.