Some sources describe Hudson Bay as a marginal sea of the Atlantic Ocean, or the Arctic Ocean.
So, my questions are: Which objective criterion could be used to settle this dispute? Considering this criterion, which ocean Hudson Bay belongs to?
But if you were to simply ask: "at which point in the continental US would water FLOW to three different oceans?", Snow Dome has the better claim. The majority of water leaving the Montana Peak towards Hudson Bay will end up in the Atlantic Ocean, not the Arctic.
If you were to ask, "at which point(s) does any water flow to all three Oceans?", it's technically the entire locus of points along the great divide between these two "triple points".
But if you had to pick just one point, Snow Dome seems more appropriate.