My cutlass has been the daily driver for the last 3 years and has survived many long distances trips summer and winter.
For the most part these drivetrains are bullet proof but wear items like ball joints, tie rods, fuel pump / filter, battery / alternator, cooling systems, wheel bearings, brake calipers / shoes / pads / wheel cylinders can leave you at the side of the road. Luckily these are cheap, plentiful and easy to fix on the spot.
Old car times that can leave you completely stranded or needing a tow can be a rotten exhaust, brake lines, gas lines and other strange parts you woundnt think about like broken springs, electrical issues, rotten rear frame. Most of these are easily caught with a dilligent visual inspection before your trip.
For the most part if your up on your maintenance or periodically poke your head under it to check things out you will likely have caught the odd ball issues at the same time and the trip will probably be problem free. Otherwards if it a neglected old car you could be rolling the dice.