It's the fact that the northern ice is melting that makes ice breakers MORE necessary not less.  When the northern ice melts, shipping wants to travel through the north west passage, but because the melt is not uniform, the presence of more shipping in those northern waters requires ice breakers to rescue ships when the wind shifts, and ice pans blow into the new shipping lanes threatening the vessels there.  As for cutting everything but SAR, that just indicates that you don't know what else the Coast Guard does.  Good luck getting your groceries shipped in if the Coast Guard wasn't out there installing and maintaining aids to navigation.  They also inspect and certify vessels for regulatory compliance (safety) and do fisheries patrols to keep out foreign fishing fleets from our waters.  Coast Guard really is the one military service without much fat to cut.