They are fairly quiet. It doesn't take as a big of a blower as you'd think. In colder climates, heating the pool heats the air in the dome. I have no idea how much energy you'd use heating it though. I saw one set up at a show in Atlanta a few years back.
wouldn't you still need to close the pool for the deep winter months if you tend to have cold winters with lengthy periods of below freezing temperatures? Or, if you were heating the water to 80-85 degrees consistently, does the cold temperature become a non-issue?
Requirement to close depends only on your climate and your desire to use your pool in winter (and related willingness to pay for heating). If you keep water flowing even slowly through pipes when temp is below freezing they will not freeze. If you have salt in your pool that further lowers the freezing point.
The big issue is are you going to keep it heated enough to use in winter? If not then probably much easier to just close until climate warms up above 60 degrees F. (I read 60 degrees is a rough threshold for closing/opening. Funny thing is this summer my pool rarely got above 60 degrees !
I live in Seattle area where we get a few weeks of freezing temperature. However it is 35-55 from October through May most years. I'm starting to look for pool domes and the bubble is a neat variation... however I need to get the deck built around the pool first so there is something to rest the structure on .