Your shoes won't come off (90-95% of the time) if they are tight, well put on, and a good fit. Good farriers are a must. My horse wears all four shoes during competition season.
Very few populations of mud are too powerful for a good shoeing job!
Easy Boots are terrible with rocks, in my experience. I had my easy boots ribbed off three times when I was riding through rocky streams in NC. I don't trust them much with mud either... Mind you, my pair was borrowed and not the most well fitted.
When riding with shoes, always carry duct tape. You can tape on a shoe with a sprung heal for long enough to get back to the barn or tape over a barefoot hoof for some temporary protection.