I will try to take some pictures of my foam boxes and post them. I have never INTENDED to use these boxes as hives (I made them as swarm traps) but when the girls are planning on swarming, what to do? So some of them have been out in the weather for a season. Here is my experience. Without paint, UV starts degrading the foam. Paint helps. I used paint inside and out, and the inside paint did not seem to bother the bees, and did seem to deter them from chewing. Lids will start to warp with time. So will the walls unless firmly attached to each other. I found that even glue alone wouldn't stop it, but that glue (There is special glue just for rigid foam) with big, long deck screws would. Duct or duck tape WILL break down (I have tried different types for winter proofing). The biggest problem is, as others have stated, that some spots are just not strong enough. Mainly where the lids meet the body, and especially where the ears of the frames rest, even with a wood or metal protective strip. It is impossible not to rip up the foam over time. That said, they make great swarm traps, and even better "I'm off to get a swarm or do a cut out." boxes as they are extremely light and plenty sturdy in the short haul.
JC