Well, you do have the problem faced by all multi hulls that the ice will get wedged between the hulls which will lock the ship in place quite handily.
Also, I believe SWATH ships like most multi hulls are made largely of aluminium.
The former I had not considered. I would expect the severity to scale with the ratio of length to beam of the between-hull dimension, which for a SWATH is pretty low compared to other multi-hulls. And the amount you're trying to move the ice scales with the waterplane area (really, the projected frontal area at the waterline), so it should be less severe here than on a traditional catamaran.
The latter may well be true, but isn't by necessity. You can build whatever you want out of whatever you want, so long as you're willing to pay the associated displacement penalty.