Rathervthan breaking ice, I fill a spare drinker with liquid water overnight and keep it in the kitchen, ready for my 7.00a.m. trip down the garden. If you start with water that's not too cold, probably the outside temperature will warm up a few degrees by mid-morning, so its less likely to freeze during the day. Also, breaking ice on drinkers may damage them - plastic ones become brittle in the cold and may shatter, and metal ones can be bent out of shape. It was -6.5 here a couple of nights ago, and when the temperature goes as low as that overnight, I don't think glycerine would make any difference unless you used so much that it would affect the water quality for the birds.
If you have an electricity supply down at your run, you can buy heat pads designed to go under drinkers, which give out enough gentle warmth to keep the contents liquid. Maybe there are solar or battery options of the same thing? However, I find the water needs changing daily anyway, and as our outside tap and the storage butt are all frozen up ATM, I have to bring water down to them from the kitchen, so it might as well be first thing!.