A true hot dog is an emulsified sausage, the fat and meat are finely ground and blended (emulsified). I would be far simpler to make deer brats with a 70/30 deer and pork fat combination. Commercial bratwurst seasoning mixes are available from several sources. I recommend a 42/44 or 40/42 natural hog casing.
I make a lot of sausage and sticks but have not messed with emulsified sausages IE, Mortadella, Bologna, hot dogs and others. Emulsified sausages are less forgiving in the perpetration than other types of projects. For the small amounts of them that we eat it is just easier to buy them.
There is a local butcher near us that has the contract to supply the meat for the Cabelas meat packages featured in their Christmas catalog. I have had many of their products. That company's version of a "Venison Hot dog" is much like a brat sized summer-sausage. They are not bad but they are not a Hot dog in either texture, taste or appearance.
I recommenced making basic brats with your commercial spice mix in five pound batches. You can vary those batches by adding to the mixed product. Another local butcher shop does this with their pork brats. No matter what type of brat you request from the showcase they all start as the same basic brat. Apple Brats have apple sauce added, jalapeno have jalapeno peppers, the same with pineapple and all the others. The sauce, peppers and other added flavors are mixed in after seasoning and prior to stuffing. Allow sausage to hang out in the fridge for the flavors to develop for 24 hours prior to freezing will improve the finished product.
Good Luck
