If you want the disposable kind (which I always do--refolding a wet poncho isn't something I enjoy), then cutting them down is the best idea. There are a few places that have slightly smaller kids' ponchos. We've bought ones with Disney characters on them for $2 each at Target close to WDW, but they still aren't small enough for a 3 year old. The only way to get one for a 3 year old is to buy ones that come in distinct sizes, and those are going to be expensive.
The great thing is that your 3 year old is probably going to be in a stroller. If you get a rain cover for your stroller, then he's good while he's in there. You'll just need him to not get soaked between the stroller and where you get into the lines, and that's not a lot of time. Depending on when you're going (how cold it will be, how often it will rain and for how long), you may not need anything at all for him, or maybe just a hoodie.