It'd depend on the pet. We had full size trees with cats in the house a lot. Just make sure that real fragile/keepsake ornaments are anchored very well and don't hang food on the tree. My friend has a lhasa apso, and he doesn't bother the tree either. Circles it suspiciously actually...

No tinsel with young pets in the house, although older cats and dogs don't seem to think that shiny hairballs are fun. Zebra finches like a lit tree. (They sit in their cages with their beady eyes fixed on all the blinking lights and mutter happily.) I don't know what a ferret or a parrot would make of a tree, though. Hay, maybe?