Yes, insurance will be more expensive, if available at all. Higher deductibles, and probably the requirement for supplemental training. For this reason, it is sometimes the case that the flying school floatplanes may be rented dual, but not taken solo, or taken solo with restrictions as to where landings may be done.
I have been told that one of my amphibians would not be insurable at all, other than I have another of the same model already insured, so they could not really say no to covering the second one. But another fellow who bought the same model amphibian (I trained him) could not get hull insurance at all. When he wrecked the plane, he took the loss.