Using sound judgement is going to supersede everything you learn in EMT school. You will not always be able to completely do things in the order that the NREMT wants you to. Do what you can.
At your school, are you learning to size up the scene by doing:
BSI
Scene safety
Mechanism of injury
Number of patients
Consider need to additional resources
C-spine
Or are you using ENAMES? The 2nd E is extrication, which some schools use too. In this case, I would consider this an extrication issue. You need to move the patient to a warmer area to do a better assessment. This is true with everyday type of calls too such as a patient being in a small room, narrow hallway, or in a vehicle where you need to move them to a better spot to assess them. This is also true if you are in a public place and should move the patient to give them some privacy too. You need to think about things to do that can make it easier to assess the pt such as turning on the lights, moving furniture, or changing the patient's position.
*ENAMES: environment (scene safety), number of patients, additional resources, mechanism of injury, extrication, and spinal immobilization/stabilization.
Do a quick assessment with them with their clothes on. Move them to an area that's warmer such as the back of a rig or in a building, and then expose.
Many calls, you are not exposing the entire patient. You will be doing a focus exam. For example, if the patient is complaining of chest pain, you don't need to take ALL of his clothes off. You might just lift up their shirt or unbutton it, look and feel quickly, and then lower or rebutton their shirt.
When I took the NREMT, it wasn't throwing tricky questions or unreasonable things. It asked mostly pretty straight forward things. Don't over think these things too much for the test itself. If you haven't done a ride along yet or you have, you should have noticed that the people you were with probably didn't do things exactly to the book of NREMT. Sometimes things were done in different order or delayed. I think the biggest most important things that are done are scene safety and ABC (pretty much scene size up and initial assessment), but pretty much scene safety and ABC are the most important of everything in my opinion and what is usually addressed the quickest.