Pfffft! Buncha amateurs! Nella girl! Listen up and listen up good! This is a very simple problem, and one I faced every year until I smartened up and put a more stout and permanent roof over the run.
Here's what ya do: Grab your push broom, [you do have one of those, don't you? Or was that Cynthia's I just saw in a picture?] go inside the run, stick the head of the push broom up against the underside of the tarps and start shaking the living bejeebers out of it! The snow will slide off, even though much of it will likely be trapped by the chicken fencing lower down. But, you can reach that from the outside and deal with from there!
Your only drawback will be if the snow has partially melted up there and then refrozen. In that case, the ice will be very well stuck to the tarp, and that means that you will have to
really shake the living daylights out of it! Sometimes I've had to resort to hitting it with a baseball bat to break up the ice and work it loose from the tarps.
For future reference, go out there and shake the tarps from the inside anytime you get up to about 2 or 3 inches of snow. The more there is, the harder it is to get off. And you definitely don't want to wait in the hopes that it will all just melt off. Overnight lows will glue that snow to the tarps just as sure as I'm sitting here!
And if you don't have a push broom, just make up a pole with a 2x4 cross piece on the end of it. Anything broad and flat will do actually. You just want to get the pressure you'll be applying to be widely dispersed so that you don't rip the tarps!
See? Living with insomnia and cold northern climates can have its useful moments!
And I still have a splitting headache!
ETA: Tim, the next time you pray for a milder winter, specify to the Almighty that he can send the snow over here! I love the stuff!!
Just don't tell my husband I said to do that! He'd clobber me for sure!