Have you previously had issues with ice damning?

This might be a big enough pain so you want to check with some other insurance companies. My company requires me to have a fence with a self-locking gate around my pool. My neighbor's company does not even require a fence.

I've never heard them called "ice arrestors" but what the insurance company may be talking about is a metal "grid" - for want of a better word - that sticks up above the slate and breaks any ice sheets into smaller, less dangerous pieces before they slide off the roof. If the side they're talking about is the one that receives the most direct sun, they are probably concerned with large dangerous loads of ice and snow sliding off and damaging things, including people, below.

I agree that installation needs to be done very carefully and the whole process is likely to be pretty expensive. There is a company in Portland that specializes in slate roofs, both new and historic, which should be able to help you.

A second insurance company is also a very good idea. Steel roofs would have the same issue with sliding snow, but I do not see any "ice arrestors" on them.