Last winter I was shooting when it was around 0deg and quite humid out. I actually had ice build up on some of my scope lenses and could not think of a way to clear it so I tried to melt it with my breath enough that I could wipe it away. You can probably imagine that was a huge mistake because my breath basically froze instantly to the lenses and made it really unusable.

I was thinking about carrying a small squeeze bottle of alcohol around with me to squirt on the lens if I ever had icing issues again. Any issues with that? Does anybody have any other remedies to an iced scope in cold temperatures?

Tape on hand warmers near objective and ocular lenses? Spitballing here, I usually just modify breathing so I don't breath on the lens, I haven't had the problem you describe.

I've never had that problem.  I've found covers provide adequate protection