What is the best way to train an Arabian on Howrse so that it will actually win competitions?

The best way is to only train dressage and speed and do short trot rides (for speed), and then only enter competitions when you have a tub of grease.

If you have now trained quite a lot, here are some tips that may help:

*use fillers to help you along

*don't enter races with higher skilled horses

in the areas which matter for that comp

*enter the lowest level comps available

*enter comps he is not so good at