Cold starting problem

I have a 1999 F250 Ford with a V-10 gas engine. It has 65000 mi. Mostly, it starts and runs great. However, when its 10-15 degrees F, it has a hard time starting. It may start and run very rough - then smooth out. Or it may not start- I come back in 2-3 min and it wil start. Once it starts and gets past the rough/missing stage, its fine. If the temp hits 25 degrees F, it usually starts just fine. There are no warning lights and I’ve taken it to 2 different car parts place and plugged in a computer- but it shows no alarm code. I’ve taken it to 2 mechanics and told them they had to work on it first thing - when its 10 degrees. Once the temp reaches 25, it’ll start every time. Both mechanics found no problem starting - I’m sure they didn’t get to the truck until it warmed up. Its hard to fix something that works fine.
I don’t know where to look, but I don’t want a truck I cannot trust to start. I’ve changed air, fuel filter and spark plugs.

The problem might be with the coolant temperature sensor for the computer. The computer determines the air/fuel mixture required at a given temperature. So for example if the sensor is telling the computer the coolant temp is at 35 degrees when it’s actually 10 degrees, the engine will run too lean during a cold start.

Tester

@HenryB Here’s my simple advice.

Have the mechanic connect the fuel pressure gauge to the rail in the evening.
In the morning, turn the key to position 2
Look at the gauge. Is there sufficient fuel pressure?
If everything’s not fine, then you have a starting point.

How old is that battery? If it’s 4-5 years old, it should be time for a new one.