The caverns will be pretty much the same temp all year round, maybe a little colder but not unbearable. It is arkansas so wheather could change drastically from one day to another. If u are planning to stay a bit, make sure there is no winter weather in forcast because its a hilly curvey road and subject to ice, not snow, wich makes travel nearly impossible. Its still very beautiful tho and worth the trip any time of the year. Only change is defferent parts of the caverns are available for tour depending on the season. No pets are allowed in caverns, but in camping and picnic areas they are allowed, but need to be on a leash.
I would say the temperature in the cave never changes. The only issue about visiting in January Would be road conditions. I didn't see any dogs. I doubt they would be allowed inside the cave unless they were service animals.
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