6 ponds total, every pasture has water. I live right above the big pond.
Excellent! That is the standard set-up of every wise rancher I know.
In addition to destroying the banks, the cattle also quickly fertilize the small ponds that they share with fish populations. If the cattle have had access to your big lake for many years, then I assume you are confident that BOW has enough water flow-through that your nutrient influx from the cattle is NOT a problem?
If that is the case, then it sounds like using your biggest body of water to fight winter ice is going to be your easiest solution.
I like your idea to limit the cattle to a single point of access. At least that should protect all of the rest of your shoreline.
There have been several past discussions on Pond Boss about cattle-pond trade offs, but I don't recall a single discussion about the best way to create a bank entry point for them to not destroy the bank and minimize the degree to which they muddy the pond. Placing cobble-size rock would protect the banks the best, yet cattle HATE that material for walking. You may be one of our best experts on the forum for that particular topic, so I am no help at all.
Once you do create your best "cattle area", a solar panel with battery and aerator may be your simplest solution to solve your "ice problem" for about 90% of a Kansas winter.
For the really cold stretches, you might try the buried/insulated stock tank solutions as mentioned above. If you installed a dedicated suction intake line into the lake during the fall, you could at least pull up in your truck with a gasoline trash pump and fill it in 30" during the first really bad cold snap.
Finally, I can't remember if your family owns some earthmoving equipment? If you have a low bank somewhere, it might be easier to excavate a shallow pond with a narrow inlet to the main lake compared to rocking off a large section of your shoreline. If you fence off the inlet, then the cattle can have their own nice pond with easy access shallow banks. Shallower ponds are cheaper to build, but will ice over more easily. However, a bit of aeration should be enough to keep a portion ice-free for most of the winter.
P.S. One of my neighbors has some old horse troughs that he uses for emergency cattle water when they can't chop through the thick ice any more. He leaves them on their sides on some concrete pavers so they don't freeze to the ground. During the worst times, he tips them up and fills them with water delivered from the back of his dually.
Good luck on keeping your cattle happy! I am never envious when I see guys around my property using chainsaws and axes on the water tanks during the coldest days of the year. Working that hard in the cold -while getting splashed - looks like zero fun to me.