Ok, you didn't specify how cold "cold" was. LP is not the most efficient of fuels, and is a very temperature dependent fuel.
The colder it is, the less reliable LP is.
Another factor is using too small of a tank, and/or the tank being too empty.
Assuming the temps you are describing are not below about 20 degrees, you have a minimum of a 250 gallon tank, and it is at least 1/4 full, then the problem is likely in the genset itself.
Are the block and battery warmers actually working?
When was the last time this unit had a good tune up?
Is the choke working properly? To check, remove the air filter cover, and set the switch to MANUAL. The choke should close for 2 seconds, open for 2 seconds, close for 2 seconds and so on, until the engine starts.