There are many reasons that an outboard motor can be hard to start when it is cold. Start by checking that the fuel tank is full of new fuel and the primer bulb goes firm when squeezing it to fill the carburettor.

When an engine is cold, less of the fuel vaporises to the point where it will burn. It isn't liquid petrol that burns, it is the vapour. To get enough burnable fuel to allow a cold engine to run some form of enrichment mechanism is added, the most common form being the simple pull choke. Some outboard motors have a solenoid choke which is activated while the key is pressed in, some have a system that is automatically activated until the engine is warmed up. This is always the case with EFI motors.

The outboard's enrichment system isn't working

In order to start when cold, engines need a way of adding more fuel to get the correct air-fuel ratio (stoichiometric ratio). This is the job of the enrichment system. If this system isn't activated or working correctly the engine will be too lean when trying to start cold. With carburetted engines, the choke is the most common form of enrichment system. Newer carburetted outboards use electical systems to eliminate the choke and EFI outboards just have the ECU inject more fuel when cold.