You are correct; there is just a thin cotton blanket (resembling institutional bed covering) on each bed.
This video provides a very good room tour, and at about the 6:00 mark addresses the bedding.
Though there are many reviews with concerns about the lack of staff, malfunctions, and other temporary issues, the bedding is the property’s standard. I can attest that there have been many nights, year round, when the down comforters have been needed at the Swan. I can’t imagine why the Swan Reserve would be any different.
On a follow-up video, there is mention of complimentary shuttle service available from the Reserve to the Swan, Dolphin, BC, and YC. The van ride over to the BC is a great option for EP visits; it is quicker and more convenient than walking to EP, or taking the Friendship boat from the Swan/Dolphin dock. I wonder if the shuttle van also is available for Swan/Dolphin guests.