Sensitive in what way? What does your horse do? In any case, whether your horse has a physical problem like teeth that need attention or a training problem you are avoiding fixing it by riding in a halter. Generally speaking, it is not safe to drive a horse in a halter.
Oh goody! Another Canadian owner!! My favorite breed of all time - I'd love to see some pics! :)
As for riding/driving in a halter - personally it depends. I found my Canadian mare is pretty sensitive to bits also, she doesn't like anything with a single break and french links she just messes with the whole time. Rubber mouth pieces she chews up in a second flat. So I had given up on bits, I trained her for riding in an Indian Hackamore. It's essentially a rope noseband, that crosses under the chin - it's for direct reining, not really clear communication for neck reining - but me and my mare love it. I line drive her in it - but she hasn't reached the carriage/cart point, I don't think I'll ever take her there though.
But I was determined with the same mindset the previous posters have had 'if she doesn't like the bit something must be wrong'. I got her teeth done again and tried a million bits and finally found that she goes best in a metal mullen mouth bit. Someone on the driving thread posted probably the best example of the perfect driving bit IMO.
This is the link to the forum: Harnessing up-------------BITS
This is the bit I love from it:
I love how it goes straight for about a half an inch before mullening out, it gives room for the gums. It's rounds out and up so there's almost never any contact on the tongue, which seems to be what my mare dislikes the most. You can put the reins on a number of places to make it milder or stronger. And it looks to be made with copper to make it extra yummy ^^ I really like that bit - wish I had it!