I used to leave the stalls open for the horses to come and go as they please, but it ended up that they would walk in from the pastures to urinate and drop manure in their stalls and then walk back out. This added to more work for me and expense in shavings, so I added overhangs to the barn instead. It was one of the best decisions I've made!
The overhangs insure that the horses always have protection from the elements. I no longer have to rush home to let the horses in when it's raining, or wake up in the middle of the night worrying during a thunderstorm. I've also found that feeding hay outside under the overhangs keeps the stalls cleaner. Another benefit of the overhangs is that it keeps the area directly around the barn less muddy. I put stall mats under the overhangs and it makes clean up very easy. The additional shade in summer tends to keep the stalls cooler. The horses seem to prefer to stand under the overhangs because it is visually open for them and they can see what is going on all around them. The openness of the layout keeps the horses calmer and happier. Even stallbound horses adjust well to the overhangs even if they don't have constant stall access.
The following website has do-it-yourself instructions for installing overhangs plus many farm building projects