So I got Hearthfire a couple of weeks back, and I have a home given to me by the Jarl of Sawnstar, which is nice because it's right in the middle of Dawnstar, Windhelm and Whiterun, so it's very practical.

However, my Stormcloak character wants a home in Eastmarch, but I'm not sure how to get a Hearthfire home here. What do I need to do to have the courier come to me and give me the letter from the Jarl? Or is there anybody else I can talk to to get a home there?

Thanks.

Do a few errands for the local Jarl and you will be eventually offered the chance to buy a house there.

Estmarch? Hearthfire allows you to build houses in the Pale, Falkreath and Hjaalmarch. In Eastmarch, you have the house you can buy in Windhelm: http://www.uesp.net/wiki/Skyrim:Hearthfire

The Hearthfire homes are only available in Falkreath, Hjaalmarch, and the Pale.

The only home you can acquire in Eastmarch is Hjerim in Windhelm, which as you probably already know comes with the vanilla game and can only be bought if you completed the CW.

In your case, since your character is a Stormcloak, you can acquire Hjerim after liberating Falkreath Hold.

Also, to get a Hearthfire home, you need to do some favors for the Jarl of the hold in which you wish to purchase the house.

The only home in Eastmarch is a vanilla home in Windhelm. Though, it takes the most effort to get.