I've been using mine with a 1-Spot along with about 5 other pedals and there is only a minimal hiss audible through my rig, but I am playing through a tweeterless sealed 6x10 cab so that is probably why! I have compared running back and forth between its own supply and the 1 Spot and I have to turn the volume way up to hear the added noise when using the 1 Spot. It is certainly nowhere near the noise my Small Clone adds when on a daisy chain (if I use a fuzz pedal, I get a huge wave of the Small Clone clock noise even if the chorus is bypassed!).
I just bought a CIOKS AC-10 isolated power supply, but have yet to hook everything up- the Freeze does require a relatively high 146 mA, so I think the Fuel Tank Jr will not be adequate. A PP2+ also has some higher rated outputs that would work.