What freezes up?? Toilet suppl?or sink supply? or tub/shower supply?? IF you can thaw with a hair dryer your pretty darn close to the freeze point. 3 foot in a water filled pipe is like forever!! IF the pipes run thru the wall before they go down, tear out the wall. If they go thru the floor before they are inside a wall, you will have to tear out a bit of ceiling downstairs. It wont take 'much' insulation,draft stopping to make ALOT of difference. IF you have NO access panel now, I would TRY to make one for future use,,,IF you can figure out the how to make it look decent.Even small 'painted like ceiling and wall' "trim "with a plywood insert also same painted. with 2 scews in it is an improvement!! bet when you get there if its a cold or windy day and you stick your hand in there,,,you MAY find the real problem quickly(like a 'crack' of siding joint or similiar shipping in air like crazy.
I once had an old house like that,checked and found a rolled up newspaper from about when the house was built. The paper said there was a new invention being tried in town that week,,,and THEY thought it would NEVER amount to anything,,,it was such a silly idea,,,TALKING movies!!!
Once you expose the area of problem, put pipe insulation on them,and make sure fiberglass or even foam or other appropriate behind that with NO air leaks to the cavity,,,and you should be good to 'go'. all else fails put a faux wall behind the pipe,,,and a cold air vent to inside heated space to allow heat in the cavity!!That can be double used as an access panel!!