The Hutts are, without any doubt, the biggest minor ''player'' on the Galactic space.
By the time of the Cold War, there is little doubt that the Hutts would rank just a notch below the Empire or the Republic when thinking of worlds controlled or economic power.
And this is without considering that the Hutts in TOR times or ''modern'' SW times are the remnant of a vast empire that ruled around 15 000 ABY, before being devastated by the Hutts Cataclysm (the destruction of their homeworld Varl) and the Crusades from the Pius Dea.
from your post here it seems you don't know much about star wars lore. The fact that the Hutts control several planets and operate many major hyperspace trade lanes make them more then just a minor player.
Yes by the time the Civil War comes around they are much smaller but we are not there yet.