I do!! I don't make any apologies for it, either, as I feel that if this works for my horse a little better, then that's all that matters.
I have a Western saddle/bridle, and an English saddle/bridle - after many, many rides, I find it's my horse
who prefers her English bridle with her Western saddle! Funny, how many times I felt like I was doing something out of the ordinary, but it seriously doesn't matter in the end. (Of course it would if she were in the show circuit or dressage training)
At a healthy age of 20, my mare has quite a history- she's been with the Mounted Guard, Search and Rescue, then a 4-H (Halter) show horse for her previous owner. All of which required her to wear politically correct tack, of course!
Now she is mine as a pleasure horse, and we have wonderful, happy, times together riding around the secluded pasture without the worry of correct bridles.....