I'm towing all the time. Last thing I pulled was a big red log splitter from home Depot. That thing was 1000lb easy, one of the larger ones and had no issue. Barely felt it until breaking time but didn't exceed 45mph. One before that was a much smaller log splitter so obviously no issue there. I've got 60k on odo and still 0 issues.
The risk would be the same, whether CVT or regular AT : torque converter damage and mostly overheating, ruining fluid. By the way, that's what pleagued those infamous first Nissan's CVT (towing or not): bad firmware heat management resulting in fluid foaming, slowly "gluing" internal components together.