Depends. I may be off base here, but seems to me that diesels rely on a certain amount of heat to run properly, and technically they burn cleaner as they run hotter. Turbocharging compresses (thereby heating) the intake charge, which could help combustion to a point. Cast iron has its limitations, however. You also mention you have a T444e. If you upgrade cooling, you may find you've altered the operating temp adversely to the point it may not run properly. For illustration....
Granted, this is a cold start video, and it won't make it run that poorly, but I can see where temp drop could affect operation. You say you have a T444E. If this is electronically managed, a drop in temperature could drive the computer nuts. I've seen that with gas engines that had a thermostat stuck open. Also, if you're in a cooler / colder climate, you may have problems with heat and defrost in the winter. I have seen this as well, also with a gas engine that might not be as picky about operating temp.
For example. I remember years ago when I drove a taxi, the idiot I was leasing a car from cobbled up a home remedy when the radiator started leaking. It was a front-drive Buick with a V6. The original radiator was two-core, he swapped in a radiator from a 90 Caprice wagon with a V8 that was three-core. Oh, sure it dropped operating temp about 15-20 degrees in the summer and the car could idle all day with the A/C on and never break 175. But one night I had to take someone somewhere in an ice storm on urgent government business, and I was having to stop the car occasionally and let it idle to warm up, because the windshield was icing over and there was no heat. When the car was moving, it could not maintain operating temperature, so the defroster and heat would not warm up.
So if that applies here and you upgrade the radiator, you may have to consider weatherfronts in the winter, but I would think any drastic temperature drops would affect diesel operation, as it relies on a certain amount of heat for proper combustion. If it were an older T444 or 7.3 IDI, I might say go for it if the IP is adjustable, but with electronic control, you may be asking for trouble.
Now, if you're concerned about temperature on hills, you might consider oil and transmission fluid coolers if not already equipped, or perhaps upgrading to larger or auxiliary ones. With those fluids you should be concerned more about heat, as oil not only lubricates, but also helps to cool. Cooler oil = cooler engine, cooler engine = cooler trans fluid (assuming your factory trans fluid cooler is in the radiator like most vehicles). And cooler trans fluid = happier trans, which could also mean a cooler engine if the factory trans cooler is integral with the radiator. If your trans is an AT545, it needs all the help it can get.
The logic here is that a larger radiator and intercooler may drop the engine temp too much, while an oil cooler and aux trans cooler may not. Say, for instance, a larger radiator might drop temp 30-40 degrees, as I have seen, where an oil cooler / trans cooler kit might drop temps 15 degrees, enough to help fight overheating in severe conditions, but not affect combustion or heater/defrost operation.
Others may chime in on this, just my $0.02.