My, albeit, limited experience of horses would lead me to conclude that any stucture should be sound and well built - these animals kick! My gut reaction would be to go all out, don't build something that will collapse after three kicks and a rainy day. If it were me, I'd opt for breeze block on a solid concrete floor that has a slight slope towards the door for drainage and then a simple 'shed-like' wood & felt roof.
However, someone did suggest bales of straw and I have seen that used to great effect and it lasts a long time. I guess you could also say it's more environmentally acceptable in a field too. Most sheep famers use straw bales to shelter lambing sheep from the harsh winds of early spring in remote places.
Ultimately I guess is down to your budget, if you own a horse, you're probably continuosly skint :-)
Ron