At first glance, I didn't see any shared circuits between the horn and A/C systems in the schematics that would make one influence the other, but I'll keep looking to make sure.
Does the "A/C" indicator light in the HVAC controls come on when you push the A/C button?
And are you also saying that the A/C system continues to blow cold air (and the compressor continues to cycle) even though the fan doesn't run? I'm thinking that wouldn't happen if the system pressure was low because of operating conditions not being met to satisfy the Triple Pressure system switch.
If those things do happen though, and the fan doesn't run, it could mean that the fan itself is bad. You can test the fan though by disconnecting it's connector and applying battery power directly to the following fan connector contacts.
Battery power (+) to connector terminal #1
Battery negative (-) to connector terminal #2