Traveling with Whole Milk

My baby just turned 1 and we’ve made the switch to whole milk. I have those Manna stainless steel water bottles that claim to keep warm beverages warm for 12 hours and cold beverages for 24 hours. I’ve never tested the claims for cold beverages in it so I’m sceptical about trying milk for my LO. We travel a lot so having it insulated properly is important, and milk cartons on the go while we are out is not always an option. I’m hoping on making use of the insulated bottles I already have rather than buying one of those “fridge on the go” totes. Any mamas with some advice? Cross posted & thanks in advance! 😊