A few thoughts:
1. Bad points will greatly affect performance as will inaccurate gaps and timing. When you get the new point set, be sure to take the time to correctly set gaps and timing, preferably with a timing light.
2. Starters generally fail when warm/hot - not cold. I would suspect a voltage problem as opposed to a defective starter.
3. There can be several issues surrounding non-working winkers. Again, since they work when warm, it seems like a voltage issue.
You don't want to be replacing parts without good reason, but you should be aware that resistor-type sparkplug boots fail with age. The problem will manifest itself in intermittent firing. If your bike has the original boots and one cylinder drops in and out, suspect the boots. They are still available through Honda. Of course, this should only be considered after you have changed the points.