Can't imaging a housing not getting in the way of the 360 degree photos/videos.
Perhaps the new Gear 360 Pro will be waterproof and more resilient to damage.
I'd like to at least be able to leave the Gear 360 out all day without worrying about it raining.
There are no housings at the moment on the market, however you can use the 360's box that it came in to shield it form the elements.
Other tricks are to use a perfectly round fish bowl or even cear cling film.
In all cases the definition is not impacted, however you can get refection off the inside of the fishbowl and 360 plastic packaging.
Personally I have used the 360 on my helmet whist skiing and snowing. I did ensure I dried it off after each run where possible. It has also been exposed to quite heavy rain, but again I made sure I dried it off immediately.
I have not done this, however looking at the construction you could put tape around the seals of the buttons/ battery door to help improve water resistance.