Some electric fireplaces are approved for outdoor use, while others are not. You can install any electric fireplace indoors, but not all electrics can go outside.
If your electric fireplace model is approved for an outdoor application, there are certain requirements necessary to protect it from rain and snow. Check the owner’s manual for the specifics on your model. Plan an outdoor installation on a covered porch or deck. Manufacturers want some sort of roof or overhang to protect it from the elements.
Keep in mind that electric fireplaces, even those approved for outdoor use, are NOT water-tight. Efforts must be made to prevent water and snow from entering the unit.
All electrical connections must be performed in accordance with all local building codes. In fact, make sure you inquire about local requirements and regulations before you start an outdoor installation. No one likes surprises half way through a project!
One other point worth mentioning here; the same goes for an electric fireplace installed in a bathroom. Keep the fireplace away from showers, tubs and sinks. Again, be sure to check with local authorities about requirements.