Suggest Using Spray Foam
Unfortunately the access to the outside of the built-in ice box is generally very limited. However, from a useability and resale standpoint I'd recommend adding insulation to the outside of the box. A good job that is professionally done will improve the saleability of the boat. A project that looks like a do-it-yourselfer will detract from resale.To add foam to the outside use only "closed-cell" foam which is available at West Marine and other places. Don't use homeowner type foam.Caution: the spray foam can/will expand for several days after it is applied while it goes through it's curing process; therefore, don't just squirt it in randomly.Access to sides of box: This is a really difficult part. In some places you will probably have to drill holes through the cabinetry but obviously this will have to be in places where it isn't normally visible, such as behind a stove or drawer.Heat loss: The greatest heat loss will be where there is no/very little insulation, such as where there is poor access for adding more insulation. Let's say you can't add insulation to ten percent of the area. Even if you add, say, 4-inches to the rest of the box there will still be a lot of heat loss through that small 10-percent portion, so, try to get coverage where ever you can.Carrying ice is no fun and running the engine to charge the batteries isn't good either. It's sure nice to have something cold to drink though so try to make the right decision and do the work properly - it'll add to the value of your boat and your fun.