Long-distance movers charge by weight, so alcohol should only contribute to these costs. If you request climate-controlled crating or packing services, expect extra charges for these as well.
Moving cross-country may be a bit more complex, but all you need is a little extra packing and planning. The majority of long-distance movers will take your alcohol—be it liquor, beer, or wine—but may require a few extra steps to keep your items and their truck safe along the way.