all very good advice so far but i will add my own 2 cents...
the fuel system is among the first thing to repair,that metal tank can be real bad it will foul the carb and lines but will also do some damage to valves and rings...that fine rst is very abrasive and will be just like a sandblaster.
points and condensor are a sure replacement...
next would be the impeller bearing...this is crutial to belt life and snowblowing ability.the ariens units have a good quality bearing there but with this ones age i would inspect it carefully.
if not replaced in time the impeller shaft will spin inside the bearing causing damage.
sometimes the shaft actually breaks just inside the gearbox.we dont usually see this problem with ariens machines but it is possible.
from there we go to belts and bushings and then maybe a friction disc.
it can add up to quite a few dollars but if you can do most of it yourself then we can help you through it.miss snowsnowshoveler can even help with part numbers if you like.
and when your done you will have a heavy duty machine that your kids will be fighting over.
later chris
craftsman 10/28 snowblower with tracks husky 372xpg chainsaw sachs dolmar bc212 bushsaw mondo trimmer monster tractor with trailer cheep wheelbarro and couple shovels and a partridge in a pear tree