So assuming it is an heater hose: I remember I replaced the heater hose once with an regular fuel hose.
If I take a look at your picture I see the tube is rusted/corroded. That was mine too. So clean it as good as possible with an steel brush so the new hose can use the 'beard' on the tube. Use an good clamp and see what happens.
Dunno if blocking is a problem, suppose not. When you switch your heater to cold, the valve is closing the coolant system = blocking the flow anyway.
If coolant problems are gone now, all is good. If coolant is giving problems somewhere else, there is pressure on the system, mostly coming from an faulty headgasket.