While Mister Freeze (or his counterpart, Mister Zero) were the more well-known cold crook early on, these two frozen felons quickly made names for themselves.
Len Snart was a criminal developing a cold gun based on a cyclotron in order to defeat Earth-One's Flash of Central City as Captain Cold. Physicist Joar Mahkent was himself motivated towards crime by a gangster who tried to steal the cold ray gun Joar had just created. As the Icicle, Joar ran afoul of Earth-Two's Green Lantern in Gotham City.
Both Cold and Icicle repeatedly clashed with their initial foes, although they expanded their list of enemies as well as allies when they joined Societies, one of Super-Villains and one of Injustice, as well as aiding fellow Flash rogues on occasion.
Eventually Cold would face Green Lantern of his world, as would Icicle facing the Flash of his own. Both men actually worked together on one occasion, enlisted by the Earth-One version of Minister Blizzard to implement a new ice age under the guiding hand of Shadow Thief for his own malevolent purposes. While kept on ice in prison for most of their careers, they often cause their foes frigid frustration.