Outdoor display 3-5" OLED or something else?

The limitation of OLEDs is that they are using power to compete with the natural - sunlight.

If you drive them hard enough to be visible under all conditions, you will be using a lot of power in a mobile application. That's why most if not all cyclocomputers still use LCDs. (I suppose some may have an optional backlight - but I haven't looked into it.)