I like that idea. We have the jar sticking up, but we do not get snow so we do not have to worry about clearing that off to replace the feeder.
In the summer it gets plenty hot though, Having it inside might help keep the hive cooler for us.
One of our brood boxes is almost all capped honey, I think we will be alright.
They are still bringing in pollen down here, so If they have not cleaned out the top super (we put the comb that we spun back in for them to clean up) by winter, we will put it in the chest freezer until spring.
My worry is that they might swarm if they do not have enough room.
Florida can be productive all year because some winters are so mild.
I have another hive body ready to catch a swarm if we need to, but I would rather they make honey and stop working so hard making more hive.