Ayup, this would happen at our house too, I have not doubt about it.
Last year I put up some live greenery on the mantle and top of
bookcase and several other locations.  Within 24 hours Sam was having
asthma attacks.  This year I'm forgoing the "smell of Christmas".
Maybe I just won't decorate at all. Last year I gave up the stockings
because I was afraid Barnabus would pull them down, bonking himself on
the head with the heavy stocking holders, the tree went away when
Hobbes joined us 10 years ago and the greenery last year.

Julie

When my old roomie put the artificial tree up for the first time and
we hung the ornaments, Mischief got into the tree.

Its a small 4 foot tree which we placed up on the kitchen table in the
corner.  Mischief was halfway up it in a heartbeat and within 10
minutes had knocked off and broken three ornaments, the cheap glass
kind.

That year we just had the garlands and lights and she left those
alone.  She didn't climb it thank goodness.

The very next year i brought out the tree and the ornaments and
Mischief inspected everything very carefully.  But THIS time I had an
idea.

The cheap glass ornaments were the kind where the holder could be
separated from the bulb of the ornament.  The previous year I had
tried wrapping the hook around the branch.  Mischief had batted the
ornament so much and so hard that the bulb just fell off the holder
and crashed to the floor, leaving the holder attached to the tree.

So this time I superglued the holders to the bulbs.....  Then wrapped
the hook around the branch.

Mischief FLEW up the tree and started batting ornaments.  Hey, what
the?  the ornaments weren't falling off!!!

Momentarily perplexed, Mischief tried another one, that one stayed
attached too.  After a while she gave up and decided to bite and bunny
kick a low branch instead.

I haven't put up the tree since the roomie left in sept 2006.  For
some reason putting up a tree when you live alone seemed awkward.
Also technically the tree was the roomie's anyway.