We've only used our resort mugs in the parks for our grey goose slushies from the cart in France and it def keeps them cold, lol! So, with lots of ice I'd think they'd last a while, but there's that whole thing of having to carry them around all day which you mentioned not wanting to do, and they are expensive to lose! Plus, really, filled up with the ice they don't hold all that much water.
We used to always start with buying a dasani bottle and then just fill up again through out the day. This trip last weekend, our hottest trip, my DD24 insisted in getting the free cups of ice water and it worked out great! We got free water in MK, EP, and DHS, and only once had not the best tasting, but not awful, water. Almost always it tasted good, and nice and icy cold! Best ones were from Starbucks - nice bigs glasses of ice water in the cute cups with mickey on them, lol. We got lots of water and only got smaller cups a couple times. We saved a bunch of money, had ice water for awhile not just cold bottle until it warmed up in the heat, and no worries about losing a mug or nice bottle. So, my advice is to get the free cups of ice water, I know we'll definitely continue to do that after doing it so successfully on our last trip!