Firstly, it depends on whether you just want to play the normal campaign with different character sprites, or if you want to create a custom campaign that makes use of different character sprites.
If you're just planning on using different sprites for the main campaign, you're going to run into issues. The sprites are a part of the campaign just as much as the level lay-out and game logic are. They're irreversibly intertwined with the campaign, and can't be changed without some serious work that I can't even comprehend accomplishing.
So let's just hope you're talking about custom campaigns (And the alternative to the above issue, that is sort of a work-around)!
Firstly, in your custom campaign, you have to unpack the assets using the ResourceExtractor.
(Copy assets.bin to your custom campaign folder, and then drag it from the custom campaign folder onto the ResourceExtractor. This will create a bunch of folders in your custom campaign folder that contain all of the HammerWatch assets. These assets will overwrite all of the native game assets when that custom campaign is run.)
Now it's only a matter of finding the Sprites within the assets (hammerwatch\editor\customCampaign\actors\player\) and modifying them.
Now, if you really just want to play through the main campaign with your custom sprites, you can download the editor files for the campaign, (Located in resources, courtesy of Hipshot), and go in and modify the sprites in that, re-pack it, and play. However, I'm pretty sure that would prevent you from getting any achievements.
If you have any further questions, or need anything I said explained, feel free to ask!