Back in the day when people fixed things instead of just throwing them away, we used to tell people who had spilled soda on their keyboards to rinse them thoroughly in a hot shower to get rid of all the sticky soda and then let it dry COMPLETELY before plugging it back in.
Now, your trail cam was on with a close to full batter I presume, but there shouldn't be enough power there to really damage the camera itself. Just let it dry completely, recharge the batter, and you should be good to go.
And on the plus side, when you finally get to see the pictures, you may find that you now have a good hunting AND fishing spot!