There are plenty of retail stores that sell ponchos which are condensed into a small package which will take up less room in your backpack or bag. They are very cheap and are a good idea, because of the frequent, unpredictable afternoon rain showers that occur quite often in Florida.
I hope your Disney vacation is fantastic! Disney takes security seriously, and we should all be glad that they do. All of us are relieved to know someone is watching out for us, keeping all our family members safe and secure, especially at this “most magical place on earth”. You might even want to give those security personnel a “Thank You” for doing a great job.