I have eight horses and I ride them all in the pastures and fields with nothing except a halter and lead rope because they prefer it and so do I.
When I take my senior horse (The Duke!) out on the trail I clip reins to the side rings of his halter and go bareback... he's a draft X so he's got a lovely back for bareback riding. This two-reins on the halter system is ideal for him because he's a fantastic neck-reiner... calm, clever and very bonded to me. I originally retired him from his bridle because it’s the only one I have that’s large enough for my stallion and I HATE resizing tack between horses.
The only time Duke goes out under full tack is when we are riding with others. This is not because I don't trust my horse but because if another rider needs assistance (Runaway horse, etc.) I may need a saddle to help them effectively.
If we leave the property my other horses all wear bridles (The stud gets a western saddle too because he bucks when he's bored, the bugger) because they are young and green and I do not feel that I can keep them safe without correct tack at this stage in their training. If a spooky green horse bolts in a bridle you've got a chance of slowing and directing them. If they bolt in a halter... Well.