Does your unit have a basement? Can you see the supply pipes going up into the exterior wall? If so, can you feel any breeze/draft around the pipes? Is there insulation stuffed between the pipes and the exterior framing (band or rim joist)? (Maybe post a picture?) These are the only things you might be able to address without opening up the wall.
A low-tech solution is to simply leave a trickle of hot water running into the sink on those cold days; that will (probably) prevent the hot water supply line from freezing.
It's not entirely impossible for one supply line to freeze and the one (seemingly) right next to it not to. The last house I owned had a laundry room with supply lines run in an exterior wall, and on extended periods of very cold days the hot water supply line was prone to freezing while the cold did not. The only solution was to open the wall and add additional insulation and seal drafts.