Depending upon tractor, there can be multiple coolers and it is common for crud to end up between two of the coolers where it is far less visible.
I have owned several generations of GMC Duramax diesel pickups and after a few years of operation, "cooling stack" maintenance is a must because in layers starting from the front you have coolers for the transmission and power steering/hydraboost brakes, A/C condenser, charge air cooler, and finally the radiator providing lots of area for stuff to hide.
When I finish mowing with my Kubota F2690 I open the screened engine compartment, pull the radiator screen, and then use my blower to blow air backwards through the coolers before blowing off the engine compartment screening and removable screen. Doing this always results in plenty of dust coming back through the hydraulic cooler after it exits the radiator area.
The LCD screen on my F2690 is easy to read but it may be angled differently than the regular tractor models. If hard to read due to sunlight, one of the computer style anti-glare films may help. All things considered, I would prefer old style analog gauges but cost wise it is much cheaper for manufacturers to integrate information needed into a LCD display.
Rodger