I believe DEAD SLOW here means VERY VERY SLOW. Dead is being used as an adjectiveadverb, much like in the expression dead stop.
So, the first line means GO SLOW – GO SLOWER THAN SLOW.
The next three lines explain why: THERE ARE CHILDREN AND ANIMALS RUNNING ABOUT.
That said, I had to read it a couple of times to figure it out. If I saw this sign, it might have the unfortunate effect of distracting me, by causing me to wonder about its odd wording, instead of paying extra attention to my surroundings.
Of course, if you are looking for comedy, there's an alternate explanation: Baby zombies and alligators!