Radio doesn't work on on cold startups until a click is heard.
 

I have a 1993 Nissan Maxima SE with the Bose system and I have noticed, especially on colder days, that when I start it up, the radio often doesn't work until about 5 or 10 minutes of driving and I hear a little click coming from that electric compartment to the left of the steering wheel (not sure what it's called) when it finally comes on. Would this just be a simple fix with a replacement of a part in that area?

Curious about the click. I was initially thinking maybe this was the CD mechanism verifying there's no CD. Common failure...it will click. Once it does, the other settings (radio) will work.

But, left of the wheel? I have to defer to someone else.

Compartment being the fuse box?

there's a relay specific to the Bose system, i think it's even called the 'Bose relay' or switch relay or something like that. that'd be my guess

There is a relay that is put in for the Bose and is used to supply the power to the speaker amplifiers. It is located on the left side of the driver's foot well, behind the kick panel (the section between the door and the firewall. There will be 2 relays there (3 if you had the VG engine) They are the same type of relay with no labels on them so you will have to check the wire colors on the bottom of it.

There are 4 wires and the colors are:
brown/blue stripe
green /white stripe
solid red
solid black

1) This relay could be getting sluggish and not energizing right away like it should.
2) The connections on the bottom of the relay could be loose and/or corroded.
3) The relay could be perfectly good and not getting the signal to energize.

Start with 2) it is the easiest. Unplug the relay and re-install several times. This will perform a cleaning action.

1) - Swap the relay with any same color relay. Right next to the Bose relay is your ignition relay. In a way I don't recommend you swap with this one as this is very important for the car to start and run. But then again, if you have a bad relay for the ignition relay, you will know it. I recommend you swap with the horn relay (under the hood in front of the battery).

3) - The signal to energize the relay comes from the radio itself. So it is a possibility that this is a radio problem. To test this, You need to connect a voltmeter to the red wire on the bottom of the relay and see if you have 12 volts when you turn the radio on. When the radio is off, the red wire will have zero volts.

Geez, I forgot ALL about those stupid relays. Always got in my way running wires into my door for speakers and keyless entry.

If OP can find out which relay, I probably have one or four laying around.