Traditionally, the reindeer stew was prepared in the deepest darkest Lapland, way above the arctic circle, by the toughest survivors, the Lapps, using frozen pieces of reindeer meat,fried in reindeer fat. The liquid part or the stew came from melted snow, and most probably, the only spice in the stew was salt. I find it hard to believe that the reindeer herding Lapps would have had any exotic spices, such as pimento (all spice) with them. I also doubt that potatoes or onions, not even mentioning milk and butter (essential parts of the mashed potatoes), played any significant part in the every day menu of the Lapps. Therefore, I believe that the the original, or the classic, or the genuine reindeer stew contains reindeer meat, reindeer fat, water, and salt. Add anything else, and you are probably mocking the tradition. However, if you go to any Scandinavian restaurant and order the reindeer stew, you will get mashed potatoes, lingonberry jam, and stew, which contains reindeer meat, water, and some, or all, of the following; onions, salt, pimento, black pepper, white pepper, beef bouillon, butter, oil, or even some herbs (Blasphemy!!), and every single one of those restaurants call their stew classic, traditional, genuine, original, or something like that.
Based on the text above, and the fact that I’m 1/64 Lapp :), I dare to call my reindeer stew as classic as any other reindeer stew. If you feel offended about that, feel free to call my reindeer stew anything you want. (I would suggest; “Slowfood survivalist’s intentional insult towards traditional cooking, minorities rights, historical facts, and anything decent.”)
But if you want to have a damn good dinner in the middle of nowhere, I recommend trying my recipe. The reindeer meat in the recipe can be replaced with the meat from deer, red deer, elk, moose, or any other four legged deer like creature, as well as the jam made out of freshly picked lingonberries can be replaced with commercial lingonberry or cranberry jam. Also, the potatoes can be substituted with some commercial dehydrated mashed potato product, but that, IMHO, ruins the taste of the stew.
If you have some more advanced cooking gear, and possibly some butter and cream/milk with you, and the aestheticity of the dish is important to you, prepare the stew and mashed potatoes separately.