Today I'm here now it's great!
Any time really the park is open from sun rise to sun set. If you play Pokemon go there are gyms and stops throughout the park
Right now through June and even July early morning is the best time to go if you don't like blaring heat. It can get VERY hot on the trails during late Summer and early Fall. Typical South Texas. The flowers are starting to bloom and it'll be very colorful soon. It's a great park all year long, but it can get very challenging during the hottest months of the year, if you are not used to being active in that kind of heat outdoors.
Any time, but not when it's raining, there are some pavan, but muddy after rain.
Spring and Summer
I agree with William but if you don't really like cold go in fall spring and summer it won't be too hot because there is alot of shade
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