In my mind I think that this is almost no longer arguable. I think that the momentum is the impulse that is available for penetration - the force times time.

If the momentum is 0.50 pound seconds, then you have one pound force available for half a second for penetration, or 10 pounds for .05 seconds, or 100 pounds for .005 seconds. And 50 pounds for 10 milliseconds which is about what I need to get through the deer.

An arrow with less momentum has less impulse to exert and will not be able to push as hard for the same length of time.

At any rate, it is interesting that there is about 50 pounds of force on the deer while the arrow is passing through it. Although not applied long enough to push him off his feet!