There's no universal answer to that because eczema can be caused by various different reasons, plus a person's genetics play a role as well. I do know allergic eczema can be made temporarily worse by sauna, but that also is "can be made" and depends on the person and case. However, sauna is pretty short-term activity, so you will know it quickly if it's good for you or not.
Take a shower or jump into a lake/river/sea. If there's an artificial pool, take a shower first or at least pour some water on you, don't wash your sweat off into the bath/pool. I have never heard of anyone wiping sweat off with a towel, after sauna. Washing yourself after sauna is more efficient than just taking a shower because the heat and profuse sweating already start detaching the dirt on your skin. Psychologically you also feel more refreshed and relaxed after sauna, which makes you feel cleaner.