The zoo is always open! Most of the indoor exhibits are open regardless of the weather, although winter is the time they tend to do scheduled maintenance on exhibits, so some may be closed.
It is a lot of walking, but you can rent a wagon or a stroller (or bring your own). They also operate a bus during cold weather called the Polar Express. It's pretty informal; you flag it down when you see it, and they take you to where you want to go. I think there's only one bus though; there have been times my daughter and I have walked all over the zoo and never seen the darn bus! If you can catch it, it's nice.
Not to miss: Tropic World (primates), The Living Coast (penguins, fishies, plus a cool wave machine), and The Swamp (gators, etc, this is a really well done exhibit). There are other indoor exhibits that are smaller and/or don't take quite as much time. When it's cold out I tend to like exhibits where we will be inside a bit longer (those I mentioned) rather than just in and out.
Tip: Food service is limited and expensive. There are no limitations on bringing in lunches. You can also plan to eat before/after. Food service is counter service only in winter.
When you're driving in, the first parking lot you're directed to is the huge one; and it's a good walk from there to even get into the zoo because you go under the street. The second lot (I think it's the South Lot) is a couple dollars more (I think, I know it is for members) but is much closer; you walk right in.
I am a Zoo member and have been since I was small. Have a fun day!
