The Night King's army cannot go into water. So how did they manage to pull Viserion out with chains? Wouldn't that require going into the water in the first place, to place the chains around Viserion?
They clearly can go in the water, as evidenced by the wights who had previously fallen into the lake that emerged to try and drag Tormund down.
So why don't the just ignore it? Probably because it does present a bit of a barrier, from the point of view of a dead and decaying body. While it might be preserved from staying below the thermocline, inert, would fall apart more quickly the more it was under water, active, and getting in then out, vs staying relatively dry in a dry (ability to hold moisture gets lower the colder air gets), cold environment. Also factor in ocean currents, rocks, reefs, etc, and you'd have your individual wight's ability to move and act being degraded through damage.
None of the wights are 100% skeleton, even ones that are relatively skeletal-looking still have some rotting flesh on them. They still rely on tissue to provide the force to move. As that tissue rots and falls off, their gait becomes noticeably more disjointed and movements more shambling.
Once that tissue has fallen apart, to a certain degree, they're useless, I think.
So it's not in the interest of the army to soak the footsoldiers, and movement is very, very slow underwater. However, given the reward and the limited nature of the body of water in question, the White Walkers thought it would be worth degrading the practical timespan of a few thousand wights to get a dragon to re-animate.
The Night King's army can go into water. They are already dead and they are not going to freeze.
What happens in the episode is:
- They fall in the water and cannot swim.
- The shore is frozen so they can either "walk out" but they are still alive.
As for how they got the chains you could see it here: How did the Wights get the chain for doing this?