According to the search results, it is possible to ride an electric bike off-road, but it is important to consider safety measures and research local laws. Some off-road electric bikes are designed specifically for this purpose, with features like suspension and durable tires. However, it is important to check local laws and regulations as some places may classify electric bikes as motorized vehicles and prohibit them from traditional bike trails (source: [Juiced Bikes](https://www.juicedbikes.com/blogs/news/e-bike-safety-checklist-everything-needed-to-stay-safe) and [ebicycles.com](https://www.ebicycles.com/best-electric-off-road-bikes/)).
Mountain e-bikes are designed for off roads and are the most appropriate for riding on rough terrains.
If you are planning to buy a bike that you can ride on any terrain, fat tires are the best option out there. Electric bike off-road is possible.