Como a monstruosa habilidade Burn afeta objetos?

Como o Burn é um dano energético (especificamente fogo) que você seguiria, na maioria das vezes , regras sobre itens prejudiciais

Energy Attacks: Energy attacks deal half damage to most objects. Divide the damage by 2 before applying the object's hardness. Some energy types might be particularly effective against certain objects, subject to GM discretion. For example, fire might do full damage against parchment, cloth, and other objects that burn easily. Sonic might do full damage against glass and crystal objects.

Se você precisar acompanhar, use a regra acima, procurando na tabela quanto HP tem madeira para a espessura do objeto e qual dureza ( Wood 5 dureza 10hp / in. de espessura )

Ou, se não for importante, use o decreto da GM para fazer as coisas quebrarem quando for dramático. Nem todas as coisas mundanas precisam ser observadas, algumas podem ser usadas apenas para dispositivos / efeitos de plotagem.

Do PRD:

Burn (Ex) A creature with the burn special attack deals fire damage in addition to damage dealt on a successful hit in melee. Those affected by the burn ability must also succeed on a Reflex save or catch fire, taking the listed damage for an additional 1d4 rounds at the start of its turn (DC 10 + 1/2 burning creature's racial HD + burning creature's Con modifier). A burning creature can attempt a new save as a full-round action. Dropping and rolling on the ground grants a +4 bonus on this save. Creatures that hit a burning creature with natural weapons or unarmed attacks take fire damage as though hit by the burning creature and must make a Reflex save to avoid catching on fire.

Prd, regras adicionais:

Energy Attacks: Energy attacks deal half damage to most objects. Divide the damage by 2 before applying the object's hardness. Some energy types might be particularly effective against certain objects, subject to GM discretion. For example, fire might do full damage against parchment, cloth, and other objects that burn easily. Sonic might do full damage against glass and crystal objects.

"wooden" não é um subtipo de objeto no pathfinder, então qualquer coisa que não seja o que as regras dizem é para o GM. Um objeto recebe metade do dano de ataques de energia e então o dano restante tem que lidar com a dureza do objeto.