It sounds like there are several problems there!
On the starting front, cold engines never like to start that much, but ensuring you have a healthy battery and clean carbs will help it.
As for the cutting out while riding, I remember a post coming up along those lines a while ago, and someone suggested that the carbs were icing up. The cold air flowing into the carburettor caused the carb to ice up, thus starving the engine of fuel. The engine heat would then melt the ice, and you could continue on. Can't remember the fix though, sorry.
Trimming your HT leads, and ensuring they have a good connection to the caps (yep, that's their name!) will certainly help too.
Good luck with it all, and welcome to the Foccer fold!