It will make the game a lot harder, but it is possible on normal. I would know since my brother did it. It does require you to be ULTRA careful - but since you could never spam heal in DA:O, it won't really cause that many problems. If you don't have a healer, focus on being as offense-orientated as possible, since you'll depend on killing your enemies as fast as possible.
I don't know why you wouldn't have at least one healer - Morrigan can learn healing spells and mages are very useful for their offensive capabilities. You can do it - but unless you are purposefully undertaking a challenge (which is laudable), you'd only be making life difficult for yourself (unless that's what you want, which is a perfectly valid way to play through a game, akin to a no-level up run through a Final Fantasy game).
Buy potions like crazy, invest in offensive skills, and be prepared to die a lot before you can uncover the tactic to beat the fights. DA:O allows you to pick a party without a mage, and it does so because it's possible to beat the game without mages. Although.... really... the mages are useful and they are some of the best characters in the game.