The reindeer sausage sandwich is an Alaskan specialty defined by the meat the grill is built around: a sausage made from reindeer, leaner and gamier than pork or beef, grilled and tucked into a bun with onions. The lean is the whole story. Reindeer carries far less fat than the meats most sausages are built on, so the sausage is usually cut with pork or beef to keep it from cooking dry, and it lands somewhere between a bratwurst and a smoked link, savory and faintly gamey rather than rich. The sandwich is not a regional twist on the hot dog so much as a hot dog format applied to the meat Alaska actually has.
The craft is in cooking a lean sausage without drying it and dressing it to match. The link is grilled over moderate heat rather than blasted, because the low fat content means there is little margin before it goes tight and dry, and it is turned to color the casing evenly while keeping the inside juicy. Onions are the near-universal partner, griddled soft and sweet on the same heat so their sugar answers the slight gaminess of the meat, and they double as a moist layer against a sausage that brings less fat than a pork dog would. The bun is a plain soft split roll, kept deliberately neutral so the sausage is the thing being tasted, and the dress stays simple: mustard, sometimes a relish, the sharp acidic counter a fatty-and-sweet build needs. This is street and stand food, fast off a flat-top, designed so the one distinctive ingredient is the part you notice.
There is not much to vary into here, which is honest to what the sandwich is. The meat itself is the variation: an elk, caribou, or other game sausage on the same bun runs the identical logic with a different animal, and the wider hot dog and sausage family changes the bun and the load around the same idea. Those are their own builds and deserve their own articles rather than being crowded in here.