There's is obviously some kind of magical force preventing crossing the wall, which would also prevent them using water. Otherwise, they could just attack the wall directly at any time. The wildlings almost burst through the gate and scaled the wall, with a relatively small force. The others now have a huge horde, that contains several zombie giants. There are even fewer men currently at the wall.
There's no reason the white walkers couldn't just storm the wall and rip open the gates, if it was just physics holding them back. If it was just a physical wall, an army made up of thousands of tireless soldiers could just storm the gates or chip away at the wall itself, until it was gone.
The White Walkers must also be linked to the land of Westeros somehow, which prevents them from boarding ships and attacking a neighbouring land or attacking from a different direction.
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