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No cup holders or pockets from what I've seen. I believe resort chairs are complementary and you can take them from park to park. If you hire a chair at a park you have to surrender it when going to another park and pick up a fresh one from there.
I suspect that the chairs are not the most comfortable (my Mother transferred to one in the petting zoo at Animal Kingdom and noted it was not a patch on her own chair).
If you have your own, take it with you (if flying it does NOT come out of your luggage allowance)
We call the resort ahead of time to ask for a wheelchair for my grandmother. It is really convenient not having to return the wheelchair at the park and being able to take it with us. Also, we have been able to get rooms closer to the elevator because of our request for a wheelchair. No cupholders or pockets though, just a grandmother to hold things for us.