I've never stayed at POR, but I have stayed at CSR, OKW, SSR, and WL and these all had towels for the pool so there should be no need to bring any. Have a wonderful trip!
They are the same size towels that are in the bathroom.
Only the main pool has towels there. When going to the quiet pools take towels from your room with you. No need to bring them back to your room they have a bin there to put the used towels in.
Just ask housekeeping everyday for extra pool towels.
We were at POFQ at the end of June. I called the front desk and they said there were pool towels until 8 pm. We went swimming one night about 10 or 10:30 and the bin was there but the towels were gone. I assume they put the last batch out at 8 pm and when they are gone, they're gone.
Although the pools have towels, I am still packing 4 large beach towels for the kids. I don't mind using the towels provided, but my kids love their Disney character beach towels.