I can't make any specific recommendations on campgrounds in Guthrie, but I can comment on camping in central Oklahoma in the spring and summer.
We have a dear friend that we visit in Enid, Oklahoma (about 70 miles northwest of Guthrie) on a regular basis. We always are in the Airstream when we visit, and stay in a campground near our friend's house. These visits are usually during storm season. On two occasions, when severe thunderstorms were forecast, our friend insisted that we spend the night at his house. All other times, we have slept in the Airstream.
Having spent our entire lives in hurricane country, we have a deep respect for the weather and its dangers. That being said, we have decided traveling in our Airstream, trumps weather fears. We will travel where and when we want. We will do our best to avoid weather dangers, but we will not let weather paranoia (a chronic condition in Florida) dictate our Airstream travels.
There are possible natural disasters everywhere that we travel. We don't want to become so concerned about these issues that the only time we use the Airstream is to evacuate for a hurricane.
SuEllyn & Brian McCabe
WBCCI #3628 -- AIR #14872 -- TAC #FL-7
2015 FC 25' FB (Lucy) with HAHA
2005 Suburban 2500 Quadrasteer (Olivia) & 2011 Silverado 3500 (Fred) with Outfitter Truck Camper (Ethel)