In a situation like a buck converter where the inductor current is basically constant and there is little ripple on the inductor, does skin effect apply? The voltage across the inductor changes a great deal but isn't skin effect only for changes in current?
Yes you are quite right. The dc component just needs wire large enough to handle the dc current. Skin effect is only relevant for the ac current ripple.
Now suppose you have 500 Amps dc, and five amps Ac.
The wire will be fairly huge, to carry the dc component. The ac ripple will be reduced to the outer surface, but because the wire is so large, it will easily have enough surface area to handle the ripple without any problem.
Where you can get into strife is with transformers, and ac inductors, and particularly resonant inductors that carry a high circulating current. That may requires copper tubing, foil, or litz wire, depending upon the power level. It is also a particularly huge problem with transformers used in switching power supplies, because it is all ac.
But for a buck regulator, or any type of dc filter choke, with any sane percentage of ripple current, you can probably forget about skin effect.
The same applies to core loss. You will probably need to run ferrite with ac inductors and transformers, because of the good high frequency performance. For dc chokes, powdered iron is far more suitable, because it can carry much higher dc flux before saturation, but is much more lossy at higher frequencies.
Design your wires and cores for the dc, if the high frequency ripple current is fairly low, the chances are, core loss and skin effect can just be ignored..