Venison sausage???

Freeze fresh and cook as needed, or cook and freeze

either is fine, but i freeze most sausage fresh

since you can add smoke whenever you want, it's not much of a decision either way

some sausage, like kielabasa for example, is gently hot smoked until fully cooked. But again, gently. Not straight-up grilled. But more of a gentle slower hot smoke for flavor and color 

And then it can be fried, grilled quickly, eaten cold, whatever. But always with the smoke and color and texture from having been fully cooked and smoked

But if you are going to grill and smoke it anyway, each time you eat it, no need to hot smoke 

I'll add that i tend to avoid reheating as much as possible, because it gets drier each time

if there's a lot of fat, like there should be with kielbasa, you don't notice the drying out because the melted fat makes up for it

sausage, especially with lean meat like venison, really needs extra fat added