So you want a phone strapped to your wrist that can be oriented vertically or horzontally? Some samsung devices sport styluses, namely the ultra phone, that you can use instead of your fingers as it can be hard or impossible to do with gloves on. The unfortunate downside to this is that your arm would get tired after long use, and you are more dependent on headphones/earbuds or speakerphone for calls. A phone attached to your arm could be clumsy for quick actions and needs your hands to be free to use, but you live with what you have.
Maybe instead, a mechanical arm that attaches to your shoulders will be more versatile as you can still do one-handed, and your arm will not get tired. Could maybe include a stabilizer in the design for great video recording capabilities.