The float bowl could be draining down. If I don't drive the truck for a couple days when it's cold, that happens to me. The accelerator pump gives it enough gas when you tromp the pedal to start it, but there's no gas in the float bowl. I crank it for about fifteen seconds with no gas pedal, then stop, tromp the pedal once or twice, and it starts right up. It takes those fifteen seconds or so to pump gas up to the carb. You can get rid of this by putting in an electric pump in line with the mechanical, and just turn it on for a couple seconds before you try to start it, but I've never bothered.
The float bowl might be draining down when it's cold because rubber gets hard in the cold and doesn't seal, for example.
A starting procedure you might try is just crank it for 15 seconds or so with no gas, then stop, tromp the pedal twice and turn the key. If it starts right up and runs fine, that's the problem.