Toy Sled

Ice Mimics are the only source, and they spawn on their own in the Hardmode underground snow rather than hiding in the chests you already opened. Clearing out a chamber down there and letting the spawn rate work is more reliable than wandering, though they hit hard enough that you want a platform arena rather than a flat floor. The same enemy drops the Frost Staff, so the farm pays out either way.

The snowman walks beside you normally and pulls out a sled when it falls too far behind, which is the whole joke. It ignores the calendar completely, so nothing stops you keeping a Christmas pet running through summer.