The description for Wall of Ice states
"If the wall cuts through a creature's space when it appears, the creature within its area is pushed to one side of the wall and must make a Dexterity saving throw. On a failed save, the creature takes 10d6 cold damage, or half as much damage on a successful save."
For both Wall of Stone and Wall of Force the spells specificity it is "Your choice" which side they arrive on, with Wall of Stone triggering a Dex save to see if they can avoid it. Wall of Ice's save only state doing damage, but nothing about getting a chance to escape.
Does that lack of specifying the caster's choice mean that it is the target's choice by default? Do creatures surrounded by the walls not get a chance to escape as long as they are untouched?
My current reading is that if a target is hit by the wall they can escape freely, but if you can enclose the targets without the wall touching them they would be trapped without a save to escape. Would that be correct?