I don't want to pay the tree service I hired.
That's bad. Why wouldn't you pay them?
I don't see why I should pay them when nothing has been done
It makes sense that you don't want to pay them yet as they haven't done anything.  Just make sure you pay them after the work is done, because otherwise they'll probably sue.
Maybe I'm a bad person, but I don't like paying. I feel like I get screwed over either way, so I'd rather just not pay them after either.
Well you do have to pay them after they do the work. Otherwise they will sue you for payment on the work that they have performed.