Yeah, quite a few people I ride with do that if we're going to be out long enough to stop for a break or lunch. I personally prefer a combination halter/bridle. It looks better and isn't as bulky as having a halter AND bridle. Blade's looks like this...
The bit unsnaps at the cheeks and you can take it off so the horse can graze and be more comfortable.
I absolutely love your bridle. ;~D
It's because of the look and bulk (and interference with my english noseband) that I don't usually ride with a halter on, I just tie it to my saddle and bring it.