The Ash Warriors' training has, according to the Ash Warriors, been passed down since Luthias the Dwarfson first harnessed the battle-rage of the dwarves. Ash Warriors harness the battle rage inside, nurture it, and draw it out so they cannot fall in battle until their last foe is slain. Ash Warriors trust their hounds with their lives, as the hounds do them, and fight side by side with their hounds in battle.
In Dragon Age: The Calling, Kell reveals that he trained with the Ash Warriors. Part of their training focuses on the belief that you should "die" before battle (somewhat similar to the dwarven The Legion of the Dead); this death is a ritual that, for Kell, involved the other warriors drawing blood from him via shallow cuts, and then rubbing salt into the bleeding gashes.
Ash Warriors are proud of their traditions; if your Warden is an elf they will show little to no respect for you, if you are a human they will simply ask you to let them be, if however you choose to be a dwarf their leader will show you great respect and be much more polite.
Given the fact that the Dwarves are given credit for the creation of the Berserker fighting style, Ash Warriors may simply be Berserkers.