According to the wiki, your running speed is 17.3 f/s. That means you run at about 11 mph. If the total area of the map was 14.3 miles, you'd be able to get from any point to any point in less than two game hours. You don't. It's a ten hour trip from Windhelm to Whiterun, for example. (Providing of course you play with the default time scale, of course)
If it were a real map, or everyone had the same size screen and resolution, it would be easy enough to eyeball the distance between the above mentioned cities, and call that 110 miles. Although your results may vary, I can guestimate that the longitudal distance of Skyrim is about 400-600 miles, and the latitudinal distance about 800-1000 miles. So, just as a rough estimate, the province would be somewhere between 320,000 miles, squared and 600,000 miles, squared.
For comparison, if we split it in the middle, Skyrim is about the size of Alaska.