Top hose is the outlet from the engine, bottom hose is the return hose from the rad. You'd expect the top hose to be hot, and the bottom hose to be cooler, - not stone cold, but certainly cooler than the top. You'd expect these hoses to be pretty firm with the engine hot, and squishy with the engine cold.
The engine over heats under load, and doesn't overheat when idling. Idling actually produces far less heat - so the problem is not the ability to shed heat at all, it is the amount of heat you can shed. The fact that the bottom hose is cold, suggests a circulation issue.
The things that can go wrong:
- The rad can lose all its fins and be less effective - in this case, both hoses would be hot. Everything is moving properly, but the radiator isn't doing its job. Doesn't sound like your problem.
- The pump can be knackered - so not pumping. This fits your symptoms. A small amount of water is getting to the radiator, it is fully cooled, but it is not enough to cool a hard running engine.
- Air bubbles - could be the cause of the pumps inability to pump.
- Blockage in the rad or thermostat - again matches your symptoms.
So - drain and refill so that there are no air bubbles (search on here for the method, I think there is a bleed screw on the rad and the heater needs to be on hot).
If not cured, then suspect pump or blockage - so either the rad is crudded up, or the thermostat is b0rked - but they normally fail open rather than closed.
The other potential issue is a duff gauge, but your description suggests it is working OK, and that there is a real problem in there.
Be careful driving it - the heads don't like overheating, and that will make the problem a lot worse (expensive....)