How do you walk from Windhelm to Winterhold?

I was having problems with this too. From looking at the map I thought that I could travel along the coast to the east of Windhelm to get to Winterhold, but there is no path for that. You actually have to go west from Windhelm then North through a mountain pass. From there you'll end up along the coast east of Winterhold. There you'll start heading west till you get to Winterhold.

For a better picture you can look at this map from the Skyrim Wikia. It may be a spoiler if you'd rather explore it yourself.

The Clairvoyance spell can be used to show you the way to your destination, even when wandering around the main map. It sometimes takes you a little out of the way but I've found it to be quite accurate.