My 1200 picks and chooses when it wants to start. The cold really gets to it, but I can't diagnose why.

I pulled the starter and alternator from the motor and tested them both. They worked fine so it was time to look somewhere else. Testing the dizzy showed a problem with the advance, so I had it recoed. It drove brilliantly for one day and that was it.

Now the engine cranks hard at first turn but won't kick, and the battery runs down quickly. It occasionally starts when the weather gets warmer. I'm out of ideas, someone help a brother out? Please?

Seems like you have checked most things. What about the carby? Sounds like it could be a fuel problem somewhere. Is the mixture set correctly?

How should I go about checking the carbie? I'll admit that I had resorted to dropping a little fuel down the carbie, but even this couldn't make it fire, at least not until the weather warmed up.

Could it possibly be a fault with the fuel pump?

if I were you i'd check out that dizzy again. Maybe a bolt/screw came lose in the dizzy and now your timing is a bit out

Check your timing, spark, high tension leads, distributor rotor, points, distributor cap, spark plug also your carby maybe your choke is not operating properly?

Goodluck