I used to have a 1967 Cherokee 160. I found that the battery flattened quite quickly apparently due to the electricity supply from the battery to the starter being made of the wrong metal or something (I believed the person who told me anyway!)
I found myself jump starting it frequently so tried several different methods and ended up doing the following.
Fuel on, prime twice, check mags off and turn prop through four compressions. Jump in, prime two more times, set throttle at about one inch, mags on, brakes on and turn it over. I found that even on -7 degree mornings it would normally fire with this method but do be quick with bringing the power back as the engine is trying to turn treacle at this point.
Good luck.
P.S If the a/c is kept outside it might be worth keeping the nose out of the direct overnight cold winds and perhaps even blocking the nostrils of the cowl the night before? This might stop the cold really taking hold.
Hope I've been of help.