Can a freestanding wine cooler be built into cabinetry?

Only if the manufacturer explicitly rates it for built-in installation with front-venting. Many models in this list (Yeego, ORYMUSE, Ca'Lefort, the FoMup and the 200-bottle dual-zone unit) advertise built-in or under-counter capability, but freestanding-only units vent from the back or sides and can overheat if enclosed. Always confirm the venting direction before installing flush.