Yup, cardboard does the trick. I am in my first winter with the Emax 25 cab and up here anything about -8C and colder it dos not like at all. I could not get to proper PTO RPM's and it would spew a stinky white smoke and it sounded very tinny. And as you said the cab heat was just warmish. So I tried covering 3/4 of the rad with card board (i think about -18 that day). Let it run for a bit and went to blow and wow what a difference. The cab nice and toasty, no white smoke at high RPM and the engine sounded 100 times better (normal).
It is warmer now so I need to be aware of how much rad i cover but so far no issues.
Other than that do how do you like the tractor?