Am I able to complete Horde mode as a single player?
Solution 1:
At least for me, the answer is definitely no. The game throws way too many enemies at you for you to be able to have success on your own. I can't imagine surviving the first boss wave (wave 10) on my own, when it throws multiple Reavers, Berserkers, or a Bromak (sp) at you.
It would be cool if they made a version that could be played by yourself, but as it stands today you need a group to hope to complete all 50 waves.
Solution 2:
There's no technical reason why one person couldn't complete Horde mode alone; it completely depends on the skill of the player. While this may be difficult for most players, it is not impossible to imagine that the more skilled players could finish it on their own. Personal experience is irrelevant.
EDIT: As a proof-of-concept, I successfully completed through the first boss wave by myself. I'm very certain that if someone had the skill and the patience to go through all 50 waves by themselves, they could.