Would it be ok to put cake in the freezer?

For fathers day I am attempting to make my father a bass fish cake for fathers day. i baked the cakes today. once they cooled i wrapped them up and put them in the freezer to get firmer for cutting and shaping in to a bass tomorrow. is it ok for the cake to get frozen hard then thaw out? would it turn out or become stale or mushy as it defrosts. would it be better to keep them in the fridge? I put them in the freezer so that when i cut and shape them into a fish the cake wont crumble. i also plant to but royal icing on top then completing it with fondant. this is my first attempt. any feed back would be helpful. thanks!