As your chair isn't a park rental (and therefore not identical to half the other chairs there) it's not that likely that it will be taken. If all you want is security, you could put a bike lock through the back wheel and around the chair. Just don't lock it
to anything, as this will stop CMs from moving it if it's in the way.
If you want to, however, decorating the chair can be fun! Last Christmas I went for tinsel in the wheel spokes and around the footplates, which was good and festive. You could also use ribbons, strings of beads, scarfs, strips of fabric or anything else long and thin that could be woven around parts of the chair (just make sure there's no chance of things getting tangled around the wheel axles). Quick warning, fabrics will absorb rain, so be warned that they will mean you'll go around dripping for a while, and that it'll make your pushrims wet and slippery until they've dried.
Another option, to do instead or as well, is to put something on the back of the chair. You could get a picture of a favourite character, a nicely patterned piece of fabric or beach towel or whatever else takes your fancy. One idea I just had (

) is to print off a Disney-related picture with lots of white space around it, and put it in a clear plastic wallet on the back of the chair. Then, when you meet characters, you can get them to sign in the white space on the paper. That's if she's into meet and greets with the characters, of course.
Another, rather extravagant option is to look for some cheap battery powered fairy-lights to strap to the chair for night-time stuff. Just make sure that everything is waterproof, before you attach it! They sell lots of light-up stuff in the parks, but it would be a lot cheaper to buy it at home.