Chytrid fungus is pretty much everywhere. Frogs don't just drop dead if they are exposed to it. Many species are completely unaffected by it, others are more susceptible (and some of those are extinct, with the species/populations still common being resistant).
With decent planning and common sense you can keep frogs outside, though you'll likely have issues with temperatures or containment; most people use glass containers for frogs, these turn into ovens in sunlight, and most options which aren't going to cook your frogs aren't secure. Keeping them outdoors is likely to result in harmful temperature swings, even if the frogs are local to your area; a cage won't have the same temperature stability as ground temperature in the immediate area and will experience greater temperature extremes and more rapid changes. If your frogs or their offspring do escape they can become ecological pests (yes, even if they're native).
I'd be inclined to set up a frog pond which the local frogs can use and breed in and keep your pet frogs inside.
