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No. If you have a good carb, with a decent engine, and it's all tuned right, such as a properly set choke, correct jetting etc, then it should start just fine
Carb's in general won't run as well until the engine warms up. It's very difficult to make the right adjustments to have them run nearly as well as FI until the engine warms up. You should have retuned the carb to put a bit more fuel into the system than you would in warmer weather. That will help some. 2-3 jet sizes should be about right depending on the temp difference and carb circuits.