Some thoughts on the matter -
A 10% cut in budget generally translates to more than a 10% cut in capabilities. It costs money to just keep the lights on, after all, and it's not like you can just fire your leadership.
Paying for the wall with cuts to the coast guard is stupid, because the wall isn't going to stop people from crossing it - over, under, cutting a hole, etc..., but it will make getting into the US via our coastlines easier. You know those semi-submersibles used for smuggling drugs? Who do you think catches most of them?
And yes, with the arctic warming up and becoming navigable, NOW is precisely the time we need more icebreakers, unless the plan is to rent them from the Russians, much like we do space capsules.