The Horde GPU Analysis
Comparing The Horde PC system requirements to all GPUs shows that The Horde is going to need a graphics card that is capable of OpenGL 2.0.

To get the best visual graphical experience on The Horde, aim to have a GPU that has at least 256MB GPU RAM.

Most bottom end graphics cards currently available today, will probably allow you to play The Horde

We are advised that 15 year old graphics cards should be able to run The Horde, but there could be a few exceptions to this rule.

Note that most games do not officially support laptop graphics cards, but nowadays many laptop graphics solutions are capable of running modern games. Whether desktop graphics cards or laptop, try searching for your graphics card to compare against the The Horde graphics card requirements chart below.