While I'd third the recommendation of the GIMP, another program I've found suitable for sprite editing is
"Ultimate Paint", which has a freeware edition and is very comfortable to use at the small image sizes Dominions 3 units use.
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Involved in:
Pax Malazica, bringing the Malazan Empire to Dominions 3.
Fate/Sprite Works, a mod including my left-over practice sprites as summonable units.