You should treat all of your cookie molds with the care you would apply to wood-handled knives or your wooden salad bowls.
If you are fortunate to own an original hand carved wooden mold, after forming your Springerle, you should brush it gently with a soft bristled brush to remove flour and dough. If necessary, scrub gently with the same brush and mild soapy water. Rinse briefly, pat dry with a terry towel and let dry thoroughly before storing. Never soak the mold in water! You may want to occasionally condition the the wood press with an oil designed for cutting boards or wooden salad bowls to keep the wood from drying out.
For resin and wood composite replica cookie presses, the cleaning care is the same. You should not apply a conditioning oil to resin cookie molds.