Is it possible to take dogs with you on an multiday hiking trips on the mountain trails through Taiwan? Anything to look out for? Are there traps along those trails?
That depends more on you than Taiwan probably.
also where. taiwan tends to be very steep. up and down. depends where you go. loads of places here are dangerous for fit adults, nevermind bringing pets. But many hunt with dogs. just depends on you and your dog.
if there is no sign at the entrance, you can probably assume it is legal. just be responsible and dont let the dog kill the wildlife.