What kind of car and which hose
Yes they can get hard and brittle. Most hoses should be replaced at least every 5 to 7 years, of course this all depends on the material the hose is made of.
If it is the top hose from radiator to engine thermostat housing then this is normal, Unless it is stuck and may need replaced, it may work park of the time and still need replaced. The thermostat will close to allow time for the coolant in radiator to cool before entering (opens) the engine and this operation is normal.