From their we site, so unless they have a sign, you should be good - but I would review the following site
http://www.handgunlaw.us/states/missouri.pdf
Zoo Policies
For the safety and welfare of our animals and visitors, the following are prohibited:
Smoking is prohibited, except in designated smoking areas
Dogs or other pets (service pets are permitted)
Feeding the animals
Entering non-public areas
Balloons
Bicycles (racks are available at entrances)
Skates, skateboards, roller blades or scooters
Loud radios
Lasers
Distribution of any advertisement, circular or handbill, or solicitation of funds or pledges of contributions within Zoo property
Personal video and photography are permitted, provided they don't interrupt the visitor experience for others
Student/commercial filming must be approved by the Zoo's Public Relations Department in advance
Wearing a costume or mask if over the age of 13