Once again, dwarves vs skirmishers... oh well...
If you exclude dale cavalery and crossbows what do you think you can do?
Head straight for the city battles, otherwise autoresolve: dwarves OWNS in autoresolve.
If you want to fight open battles, or you are forced to, try not to end the turn in open plains, but follow the hills. ALWAYS include crossbows and mercenary cavarly (i don't care if you want to exclude them, you simply CAN'T). Ignore light skirmishers and archers (like snagas or orc archers), annihilate the rest of the enemy army. Then spread your formation and chase them until they reach the map limits. If you don't have much units to chase them all at the same time, chase them one after another.
You will suffer losses, but it's inevitable. Anyway, your high armor will help, and if you are smart enough to use other units to keep the enemy under pressure and you don't show your back at the enemy missile units, you won't lose too much warriors.