There is a LOT of info here about the real and/or perceived velocity losses of shorter bbls. Bottom line tends to be, it depends. But generally accepted rule of thumb is ~50fps/in. But again, it depends.
I don't know that I see any real advantage to a short barreled rifle for what you describe, especially if you're hunting on the tundra. The short barrels really shine in snap shooting in thick timber, etc.
I go into some deep dark spots with my 20" barrels and have no issues.