In 40+ years of loitering around transmitter sites, I don't think I've ever seen an AM site where the transmitter shut down because the tower was iced up. That said, most of my experience has been with standard base-insulated towers. I've heard of sites with shunt-fed towers that did not work well when the skirt wires on the tower were coated with ice.
You probably have a lot more experience on this than I do, but I don't remember reflected power being a huge problem for AM's. The antennas just got detuned when covered in ice. I'd heard of an occasional AM tower being brought down by ice, but that's about the only time I've ever heard of ice taking an AM off-air outright.
Our big cash-generating FM is on a tall tower, with a broadband panel antenna that just seems to shrug off any ice detuning issues.
I worked at a cluster that didn't have any antenna de-icers, and our FM station that ran on a solid state transmitter didn't seem to have very many problems with ice or VSWR. The problems were the two FM's that had tube type transmitters. Reflected power could come back and burn the filaments. They had what was essentially a safety valve in that the transmitters would shut off automatically when the plate current climbed above a certain level, but that was, in the minds of management and programming, only slightly better than the filaments burning up. After all, we'd still be off-air and not generating revenue. When icy weather was a problem, we were always told to take meter readings every 30 minutes and lower power if plate current or VSWR got above a certain level.


