We actually have two deep freezers in the house, one for summer, and one for after hunting season, and another back at camp that runs on the generator, so if it's a warm year I can load quarters in there and not have to go out early.
You can put a lot more in a chest freezer, than an upright, but it requires some organization to avoid having to dig for stuff. You usually have a couple of baskets on top that we use for burger and other stuff you tend to use a lot of first. Roasts in the bottom, cause you need them less often.
Will it fit in your four cubic foot? It might if it were a chest type but it would be tight, but as it's not, I very much doubt it. Shelves mean waste space, and stuff that falls out when you open the door if you load it too heavily.
Frozen meat in roundish packages does take up a lot more space than it did before freezing, but two average deer will fit in a small nine cubic foot if you don't have things like sausage that add pork etc and expand the volume of the meat.
I grind my own burger and add minimal or no pork unless it's an older deer. So my estimate is based on that.
Get a big deer, and you won't get two in there. The 220 lb buck I got last year more than half filled it.