No doubt big hands help swimmers, but your talking about bigger hands on individuals that are roughly the same size. A moose is roughly 10 times larger than a pronghorn (800-1500 lbs vs 80-150 lbs), so it is less clear to me that having bigger hooves equals faster propulsion. I'm not saying you're wrong. I'm saying that to truly answer this question, you need to know the surface area of the hooves, power per leg stroke, and the drag caused by the water, and then apply the net forward force generated to the mass of the animal. It's not a runaway that the moose wins in water because it has bigger hooves.
Keys wrote:
I have got to believe that a moose can swim faster than a deer.
Q: Whats the propulsive force for when they are swimming?
A: Their hooves.
Moose hooves are more than twice as large than deer hooves, so I feel a moose can move through the water with a lot of power over the deer. (just like a lot of olympic swimmers have larger than normal hands and feet)
I think the best choice for a deer species is the 'Key Deer'. It is a type of whitetail deer that lives in the Florida keys and they are adapted to swimming from island to island.