There is a sign that says the trail is closed during and after storms, but I love running in the rain. Is this enforced or could I come to the trail durin a rain?

Honestly there have been times when the trail has been bone dry but with a sign out that the park was closed. It depends on where you are in the preserve. If you use common sense you will know when you should stay off them.

If there is a heavy storm many trails will be washed out and unusable. Even if they close the gate you can still get in on foot.