Have you tested compression on your motor?
Motors that have low compression are hard to start cold, but run fine and start up fine when warm. When warm the motor still has gas charged fuel mix in the crankcase, so it starts easily. Lower compression motors will run fine when warm, but have slightly less power. Having compression in the low to mid 70's psi could cause these issues.
When the motor is cold with lower compression it is a lot more difficult to create a negative pressure in the crankcase and pull in an adequate amount of charged fuel mix for starting.
Just thoughts, please consider checking your compression. If your compression is low then we would need to investigate as to why.
Second case: Please re-evaluate your ignition system. It could be running on one cylinder, so that is something that could create hard starting when cold.
Also be methodical with engine diagnostics, even when it seems to just fuel delivery..
Remember first check compression, then check spark with a gap spark checker (min 1/4 spark jump), and then carburetor/fuel delivery. Please check in the order listed.
Hope it is something simple!!
David T.