Yes, sorry, that should say vertical not horizontal, since that's what they already had. Interesting the horizontal have worked better for you. I wonder why.Those copper things are designed for the vertical nipples, I don't think they will work with the horizontal nipples. The horizontal nipples have worked MUCH better than the vertical ones for us. Haven't had them freeze up yet, down to -9F, whereas the vertical ones froze up around 20F. This was using a deicer device in the bucket, which kept the water around 40F.
You might try not using the thermocube and just turn the aquarium heater to the lowest setting and see if that works. It worked for us with the vertical nipples to much colder temps. Perhaps the thermocube is turning off the heater too often.
Other than freezing nipples issues, the main reason we switched to the horizontal ones is our birds were getting wet every time they drank from the vertical nipples. Frostbite, minor at that, but not good to have wet birds in freezing temps.