If going outside into the cold, I would consider running it high indoors, tee in a vacuum breaker at the top, and then go all down-slope after the vacuum breaker. That way, during freezing, the pipe clears before it has a chance to freeze.
For reference, here is what I was referring to with the barb fitting going down and then the tube looping up:
As for the drainage going outside, here is what I was referring to. I don't know how I would put a vacuum breaker onto a hose or if it would even be necessary?
I said double wye, but it's actually a triple wye, and just the one is used for now. This is how it's sealed:
Then it goes down part of the half wall on the insulated side of the house, and then outside, and down the 4" pipe. When it's light out, I can take a picture of it tomorrow, but it basically looks something like this (except it's coming out of the siding and not concrete like the picture shows):
So would I really need a vacuum break?