Not to jump on the same soapbox but in Texas we wait 24-48 hours depending on the trail. With persistent droughts the trails really need to recover from rain. Most are built on small creeks that can flash flood so it is dangerous to get caught in a storm, plus we don't get much rain that isn't accompanied by thunder and lightning.

That being said the one thing is make sure to thoroughly clean your drivetrain and be careful, some puddles are way deeper than you think. So just go through but be aware they could be hiding obstacles like rocks, holes, etc...