Not as described...
Icebergs are frozen fresh water. And presuming that the ocean is roughly as dense as it is now, an iceberg has roughly 1/10th of its total volume above water.
A Spherical House will in this case be mostly underwater, with a small slither above the waterline, which sounds fine...
But that's not the problem, the problem is that it is a spherical house which means that its inherently unstable and will roll. That means that the piece above the water line will fall below the water line.... That is when the ocean will decide to occupy the center of the house.
Ice itself has a weight of about 919 kg/m³. That is pretty heavy, but pure water is fair heavier at 1000 kg/m³, and sea water even more so at around 1025 kg/m³. Carving out enough space in the center to support a workable house, also means carving out enough space for the intruding sea water to overcome the ice's buoyancy.
To solve the capsizing problem means that this house looks far more like a ship.
- Lowering the center of gravity
- passive anti-roll systems such as fins
- active anti-roll systems such as pumped ballast tanks
Temperature
The next problem is that ice melts, and water freezes.
- When the water (or air) around the iceberg becomes too warm the ice will melt.
- When the surrounding water is too cold, the ice will grow.
When it melts it won't melt evenly, and when it freezes it won't freeze evenly, this will likely unbalance the weight, and eventually cause a capsize.
Not to mention the house might find itself part of an ice-shelf.
And even more insidiously. Water expands when it freezes.
- If the water managed to get close to the house component it will do damage.
- If the water expanded along a fault line it could crack the ice shell, permitting water to explore the new region.
Making it work.
The truth is that ice is not a very good building material on a planet which permits it to be in any one of the three phases.
You might be able to get away with this on a planet with seas made of another liquid, such as Titan's Ethane/Methane lakes. There Water is always Ice.
Otherwise the best technique would be to build an igloo on the ice sheets/ice bergs themselves. Moving further north and south with the seasons.