You might be right, but look at dogs, for example the American Eskimo or German Spitze below:
Why is its mouth open? Because, it is feeling hot (yes, it is standing in the snow), because dogs lose heat through their tongue, and very little via their body, including the appendages. This is more pronounced in case of those with more fur.
Now let us look at the woolly mammoth and the elephant:
What you are saying is probably correct (I was probably wrong), that the woolly mammoth has smaller ears. However, they also have a lot more 'wool' on their body to preserve heat.
So, the analogy that increased surface area leads to quicker heat loss is correct for the heat sink of a motorcycle engine (below), it does not hold true for all animals.
Now, compare the ears of an Indian stray dog and an arctic fox. Do you see much difference in size?
Finally, check out a Siberian Tiger and a Bengal Tiger: