I haven't done a drip system, yet, but I've been thinking about it for a tank in my basement. My thinking is a half gallon drip an hour (assuming I read that right) of cold water would be hard pressed to cause any kind of noticeable drop of temperature in 300 gallons plus of 75-85 degree water. You could probably throw the 12 gallons of water you're dripping daily into the tank all at once and maybe the heater might turn on for a few minutes.
I'd just tap into the cold and reduce the risk of minerals from the hot water. There's gotta be some good references out there regarding this. There are some handy calculators out there that give a rough idea of how much water you'd actually be changing out over the course of the week. A half gallon drip every hour doesn't necessarily mean 84 gallons of old tank water gets changed out weekly because a portion of that new water will be going out the overflow along with old water. You might find yourself bumping the drip volume up, still don't know if cold water would be an issue in most cases.