Or is it massively more difficult to solder new memory into a laptop than it is to solder some simple electronics project?
Yes, it is; although "massively more difficult" is almost an understatement. It's an entirely different process.
Take a close look at the Macbook Air motherboard. The RAM chips are the four large components in the red box on the left side.
You'll notice first that there are no visible solder joints on these parts. This is because these parts are mounted to the motherboard using BGA technology — the solder joints are all on the underside of the chip. They cannot be attached using a soldering iron — they are typically attached using reflow soldering, which requires specialized hardware that you almost certainly do not have access to. Inspection of BGA joints is typically performed by X-ray… which you probably don't have access to either.
You'll notice as well that there are no available positions for additional chips. Assuming that Apple uses the same PCB design for the 4GB and 8GB models — which may not be the case! — you would likely have to remove the existing memory chips and replace them with compatible higher-capacity parts. This type of rework is extremely risky; the PCB is not designed to be reheated multiple times to remove and replace parts, and the heat cycles involved may damage the board, especially if inappropriate technique is used.
As if that weren't enough, it's not even clear the machine will recognize, or even be able to use, the new memory even if it is attached properly. Standard computer DIMMS contain a small EEPROM (the SPD chip) containing data on the type of the memory present, and the timings necessary to communicate with it. This part is not appear to be present on the Macbook Air; it's likely that the timing information is stored somewhere else in the system. Since this is not a user-serviceable part, there is no documentation available on where this data might be, nor how to update it to represent your new memory.
TL;DR: It's impossible. Not just difficult; seriously, it's impossible. If you need more memory, you'll need to replace the machine.