More than one
The force field would be detected as a temperature bubble. An area of so many cubic feet of whatever temperature. Dropping to absolute zero is detectable, and so the ship powers up as far from the intended target area as reasonably possible. Once frozen, the bubble is detected at the temperature they want the ice to maintain. In other words, not detectable, or at least not easily. After formation, the ship uses a combination of lasers and sonic frequencies to break the ice. Kind of like a sculptor, making an ice cube into an iceberg. The lengths of the tubes help get the base pattern down.
The hull is the heat sink for the ship at the beginning. The formation of the ice keeps the hull cool. It would be a controlled battle between releasing the heat in the hull and freezing the surrounding water. This is done by the computer for maximum efficiency, but there would be a pretty wide margin for error if a human wanted to do it. Worst case scenario, shut everything down and try again. The ship would cool in the water. The ship creates its own heat sink.
During the initial power-up process, the water running through the tubes is the primary coolant source. By the nature of what water is, its temperature range is limited, no matter how much energy is applied to heating it. Liquid water cannot go above 212 degrees, no matter what. I don't know the limit of gaseous water, just that it has one. (Or does it? I'm not certain now) No matter hot it was when it went in and no matter how hot it became inside, it would still be less than the melting point of the hull, and thus, cool it down. Hard to believe that superheated steam could be used as a coolant, ya know? (Not saying it would ever be superheated steam in this scenario, just that it could be done) It does get uncomfortably hot in the passenger cabin during this process, but no one has yet to pass out from it. (knock on wood) Once the ice is formed, the heat from the hull is released back into the ice, and through the tubes.
The water bubble around the ship would be unavoidable by this method. This would give it the ability to move through the ice, however. Four tubes on each octagonal side, one each out of the top and bottom. All of the side tubes retracted. Push the front tube further into the ice, and use it to pull the ship forward. With the force bubble raised, the heat of the hull would melt the ice in front, at the same time it was refrozen in the back. It would move not unlike, and not much faster than, an inchworm through the ice.
The passenger cabin is in a sphere, weighted to stay level, like the ball in a compass. Water runs through the tubes into this chamber, and the ball floats in it. Also, a spongy layer for shock absorption. Water runs through the outer layer of ice, where it's pretty slushy, not frozen because of the constant movement. It gets into the sponge chamber, and the rest of the ship, as a constantly moving coolant. This melts it and heats it back into water. It then gets pumped back out. By the time it gets back out, after having gone through the ice mass once again, it's back to the temperature of the surrounding water.
The Macro Micro Fission Fusion is in one end, the force generator is in the other. Whole ship is full of water, aside from the crew cabin. However, it's also pretty neutrally buoyant, as the hot water inside weighs weighs less than the surrounding water. Both ends have a magazine of torpedoes. These can be fired from any tube. If I say one tube can do it, they all can do it. In storage, the torpedoes are about the size and shape of bowling balls. A tad oblong, though. When fired, they roll out of the tube, and when in the water, employ the same flexi-straw technology as the tubes to stretch out. They attack the target. Far from pinpoint accuracy, however. Tell it to hit the ship, it WILL hit the ship. God only knows where though. What difference does it make, as long as it goes down, right?
It could conceivably attach itself to the wall via the tubes, and pull itself through an ice shelf, rather than forming the ice. When it got to where it needed to be, it would generate a series of sonic shakes to break the ice shelf off. Detectable as a minor tremor, not uncommon in arctic regions. Even as an iceberg, it would still move much faster than the inchworm. Then proceed to destination. Or, if it needed to escape, join the iceberg back to the wall, and inchworm through the ice.
To release from the iceberg, just undo the mooring clamps and retract the tubes. The ship will inchworm its way out though the force of gravity. It even (mostly) seals the hole. The hole left behind would be just larger than the exact size of the ship itself.
When you got to where you needed to go and were planning remain stationary for a while, turn off the temperature maintenance device, and the ship would naturally freeze back to the ice. Use the water running through the tubes to cool everything else.
Does this too badly violate the laws of physics for you?
(Doing Therapy)