Problem statement: Irrespective of the total amount of snow received in the northern Plains in any given winter, drifting can cause all standard fencing to disappear in one storm. Then the dogs have free access to the county road....and the entire county for that matter! Raise portions of the fence with bits of snow fence or netting and it simply becomes a catalyst for more drifting and itself vanishes after more snow and blowing.
So the question is, can you simply put grounding rods of an electric fence charger directly into a snowbank (not into the frozen ground) and have the circuit connect to the...."bad dog!"....when it tries to get past the hot wire strand placed over the drifts? Would the current move through snow in this manner or is it too 'porous'? It would be much easier to simply raise the single strand of hot wire to accommodate additional drifting as it occurs than to continually add more fencing. It is not unusual for the drifts to achieve a height 10 - 12 feet higher than ground level....that's a lot of buried fencing!
“The most important decision we make is whether we believe we live in a friendly or hostile universe.”― Albert Einstein
In my experience snow is a really crappy conductor or a really good insulator depending on how you want to look at it. I don't think putting the ground rods directly into the snow is going to achieve what you are trying to get done. You might look at getting some of the really tall fiber composite poles (like 10ft tall) and extending your fence height. You could slide the top hot wire up the pole as the drifts get deeper then move it back down as the snow melts. Not a lot of buried fence that way, but plenty of work to stay up with it....