We do not know. For macroscopic wormholes, the classical solutions to Einstein's equations suggest spacetimes that look like ours in terms of their having 4-dimensions. For quantum wormholes of the kind postulated to exist at the so-called Planck Scale, they may indeed sample spacetimes with drastically different dimensions. This is all speculation and no one has ever discovered a wormhole, so the critical experiments to confirm these fanciful speculations are not in hand.