Bath faucet

We parked my trailer at home in the dark which was challenging because I back up on my drive next to the house through two gates. I have full hookups at home so I connected them as the temperature was forcast to be a light freeze. I left an electric heater running and decided to trickle the bath sink cold water faucet. When I checked the next morning the sink top was covered with water. Apparently with the cold water on, water leaks past the bottom of the hot water faucet. I decided to replace the faucet set with one of higher quality because the original is junk.