This is from a personal standpoint--my views here probably don't reflect the views of the majority of the staff team, but as a frequent user of the arena...
I'm not sure if anyone else has had this issue, but I've been kicked for flying several times after the snowman hits me, leading to a combat log death.
Regarding invincibility: It's so that if you fall in accidentally you won't lose your stuff. However, this is extremely annoying when trying to surprise other papers as you have to wait ten seconds. In order to replace invincibility with a similar effect, I suggest removing the benches by the top terrarium fence, and make a wall you have to jump over in order to enter the terrarium (as opposed to a nondescript hole in the ground).
Regarding the ladders: I don't find it too hard to keep players off the ladders as long as I don't use a bow or a kb sword--obviously this isn't ideal and the ladder side protection should be replaced.