You can look at a couple things.
First the choke. Take off the flame arrestor and look at the choke plate. When cold, it should have a small gap between the choke plate and the choke horn. Probably 1 or 2mm (over here it's 1/16 to 1/8").
To adjust you loosen up three screws around the circumference of the black plastic choke housing. Turn the housing so that you get the 1 or 2mm gap when completely cold.
Turn the key on (don't start it) and you should see the choke slowly open up. In about a minute or so it should be straight up and down.
If it doesn't have a full swing to completely open after being properly adjusted or you can't adjust it properly, the black choke housing/spring should be replaced. They do wear out with age. The choke can make big difference in cold starting.
Might also just need a good tune up. Plugs, points, condenser, cap, rotor and well adjusted timing.
Do you pump it when you start it? When cold, pull engagement knob on the throttle control and give it two or three pumps to start. Common practice for a cold carbed motor.
I wouldn't think you have a water or condensate issue. This is a carbed motor so they can be a little cold blooded when they start cold.