I'm going to have to try to answer this question from a mathematical stand point. If an average horse weighs in at about 1,000 pounds, and a reindeer weighs in at around 200 pounds, then a horse weighs roughly 5 times that of a reindeer. So an engine at 350 horse power (times five) would be equivalent to roughly 1750 reindeer power. That is if you are not putting Santa's magic dust into this equation.
This sounds like the most logical answer to an off the wall Christmas question that anyone could possibly hope for. Therefore I'm going to select this as the best answer. This selection was also helped by the fact that this was the only answer.
Ha, when I read the question I just had to laugh and of course then needed to look up the average weights of reindeer versus horses. You're logic is sound, but from the wikipedia article (we know how reliable that is), you're little low on the avergae weight of the reindeer.