My old trainer had a half in half out arena, the covered part was a coverall (the canvas stuff). To tell you the truth... It was AWFUL it was always flooding and impossible to take lessons in. She ended up using pea gravel as footing, but it still majorly flooded. She never had that problem until she extended it out. She took out the northern part, which was only a gate and wooden board, there was not a complete wall there, and then put footing down and fenced in a 60x40 area.
“Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen.” - Unknown