Just a tip for yourself and walking on ice. Believe it or not, slipping an old tubesock OVER your shoe/boot, mainly at the toe, will give you a decent grip. Not enough to go running or anything, but you will be able to walk a little easier. Works on solid sheets of ice.
For the horses, they are pretty smart about not running when the footing isn't too grand. Problem is when you keep them up all the time and they get full of energy so they may overdo it when they finally get out. Mine have 24/hr turn out, and choose to stay in most of the time if the footing is bad, but do venture out to stretch their legs throughout the day. Yes, the potential to slip or pull a muscle is there, but I'd rather them take it easy a few times a day vs. being cooped up and running full speed later on when it's muddy.