The top radiator hose should be hot while the bottom radiator hose should either be cold or just somewhat warm.
The bottom radiator hose returns cooled coolant back to the engine so it should not be hot but the top radiator hose should contain hot coolant and should be hot.
When an engine is warming up, the thermostat is closed, and neither the top or bottom radiator hose will be hot.
Once the thermostat opens, hot coolant will flow to the radiator.
The top hose will be hit, and the lower hose will be somewhat less so.
The engine needs to be really hot and almost overheat before the thermostat lets the coolant pass by.
If your car is not overheating, but the lower coolant hose is cold when you feel it – it may just mean that it is not hot enough, and therefore there is nothing wrong with your engine.
The hot coolant enters by the top hose, is cooled by the radiator and then cooled coolant re-enters the cooling system from the bottom hose.
The top radiator hose is usually but not always the location of the thermostat.
Either way, the top hose gets hot after the thermostat has opened.
The time the thermostat takes to open depends upon factors such as: Coolant temperature.