OK. So if you want to try to diagnose yourself for fun/interest it's very doable with a few inexpensive tools. You might be better off taking it to a shop but even they are wrong sometimes (which is got me started in working on my ac myself). Here is some background info, which is needed to be understood before troubleshooting:
First, learn the ac cycle and the accompanying equipment in your car. It's very simple (with a twist).
1) Starts with compressor - this compresses the refrigerant from a low pressure to a high pressure high temperature gas.
2) From the compressor (small line) the high pressure hot gas is routed to the condenser - typically on the front of the car (looks like the radiator, normally behind or in front of it). The condenser cools the high pressure gas into a high pressure liquid and routes it to the expansion valve (this line is also referred to as the liquid line).
3) There are two types of expansion valves. One is a fixed orifice type, located typically inside the liquid line itself, a very simple plastic/metal metering device. Another type is the Thermal Expansion Valve aka TXV. Both serve a similar purpose.
4) From the expansion valve the refrigerant flows into the evaporator where it has expanded and due to physical laws of nature (aka Magic) lowers the temp and air from inside the cabin flows over the evaporator and into the cabin.
5) From the evaporator, the refrigerant is a low pressure gas and goes back into the compressor to be compressed again repeating the cycle.
Note: There is also an accumulator (orifice tube system) after the evaporator and before the compressor on fixed orifice systems or a receiver/dryer between the condenser and expansion valve on TXV systems. A quick look shows the QX4 has a TXV. The receiver/dryer serves as a means of continually supplying the expansion valve (TXV) with refrigerant.
OK, so now that you have got the basic theory, you can see there are many different parts that go into this. You have stated that the blower motor in your car works fine, just no cold air. So that means refrigerant is not being cycled through the evaporator.
So, the first basic question is, does the compressor come on when you turn on the unit on the climate control system? You will hear a click outside the car and the clutch on the compressor will pull in and rotate the unit.
There are various flow charts available that help you pinpoint the cause, or at least get a basic idea. Knowing the components and what they do is a great start.
Example, it's possible the compressor isn't turning on. If so, there are numerous reasons from low refrigerant level to a bad high or low pressure sensor to a bad radiator fan relay to a bad climate control button or relay or wiring, the list goes on and on. In most cases they are fairly easy to test, either by using a multimeter to verify 12v at the harness or jumping the sensor, you just have to know what and where to look.
If the compressor turns on it means there is refrigerant in the system (most likely) but maybe a blockage in the system, or the compressor is not outputting anymore due to age, again numerous factors...