Harlan,
If simple siphoning isn't working (which it should because it's pressure in the tube, not gravity, driving the water flow), try this:
veterinary stomach pump - this is how we do it when we need to move fluids/mineral oil / other stuff like rumen contents / etc from the bucket on the barn floor into (or sometimes out of) the horse stomach /cow rumen (or dog on the exam table) (skip ahead to around the 2" mark):
hand pump video So, for your needs, you could carry this metal hand pump out to the ice hole, place the sucking end (bottom) into the ice hole, and the expelling end (the little needle-nose structure at the base of the handle) with plastic tube connected into your water bottle.
Basically, the ice hole would be like the "bucket on the barn floor" and the water jug the "horse's stomach".
Here's a link to an example pump:
pump and the tubing:
PVC tubing It's fair to argue though that you'll be pumping through a 10mm diameter tube instead of pouring - pick your poison I guess.
Thanks for your videos!