To make corner posts for a model horse fence, glue one post at right angles to the plain center of another post, before you add the base supports. The corner post will be able to hold rails in three directions , allowing you to join it as a T section if you wish.
To finish the fence, fit the rails into the slots on the posts. You may get a better fit for the rails if you trim off the rounded ends of the craft sticks you use as rails. To hold the rails more easily in the slots, but still have them removable for storage, you can put a tiny amount of blue tac or museum wax into the base of the slot to help hold the rail in place.