All the cooling system hoses will go soft and then fail leading to over heat and engine damage.
If enough Power Steering fluid in in the cooling system the engine will over heat and fail.
Drain all fluid, use dish washer soap and fresh clean water and run until engine at normal operating temp. Do this twice and flush with fresh clean water three times. Refill system with specified coolant.
If this is the very rare kind of car that has power steering cooled by radiator the power steering pump and gear (rack and pinion assembly usually) will fail.
That is a cooler for the power steering fluid.
Never seen a power steering hose connected to the radiator. Transmission fluid hose, yes.
NO just Coolant
check the power steering and brakes "mini-radiator" that hangs below the radiator. usually gets hit with all the weather, can be replaced easily.
The power steering reservoir is on the power steering pump.Looking from the front of car it is on the passenger side on front of engine. just to the right of the radiator recovery tank.
Those two are not connected, the shroud is on the radiator and the power steering reservoir is on the motor.
Power steering fluid, because of the friction, requires cooling. Sometimes this is done by putting cooling fins on part of the pipe that the fluid runs thru. Other times there is a small loop with cooling fins like a mini radiator next to the power steering pump. And finally the design may actually bring the power steering fluid through a loop that is actually inside the radiator to allow the coolant to cool it. The coolant and power steering fluid never mix, just exchange heat. More typically, it is actually the automatic transmission fluid lines that run to the radiator for cooling.
On the left side of the engine compartment there is the reservoir for the power steering fluid. Make sure that you do not put steering fluid in the radiator reservoir.
it will be difficult to turn your steering wheel
It's the power steering oil cooler.
On top of the radiator right next to the fan
The hydraulic seals in your power steering will be eaten away by engine oil. Your power steering will start to leek and eventually, it will not work at all.