1998 Honda Accord overheating engine

I want to flush my engine with a garden hose. It will be under 30 degrees tomorrow and I want to know if running the engine with the cold water will cause a problem?

In the last month, I had a clogged radiator that was the first cause to my over heating. I changed the radiator and thermostat. The engine was still overheating. I then changed the fan switch and temperature sensor. The since then had stopped overheating, however the upper radiator hose burst a week later. And a week after that the heater hose burst. I have changed both as well as the radiator cap, thinking the cap could have been the cause I started to see the original clogging in the radiator I seen initially. Now I want to flush all the aftermarket coolant out and fill my radiator with the Honda blue factory coolant. I would appreciate an answer to my first question as well as any additional information you can offer. Thank you.