I've used HOG, Dive Rite, Sherwood, Oceanic, and Aqualung under the ice.
Ice Diving is not much different from the bottom of Lake Erie. Temps under the ice will not get colder than 36-38 degrees in fresh water. Salt water may get down to as low as 28-30 depending on salinity and currents.
I wrote the DGX service manuals.
While regs may not be rated by the US Navy or other bodies for "ice" diving, I've seen Aqualung Calypso's being used for it after the IP was reduced to lessen the flow rate. Freezing usually occurs because of the amount of air moving through the reg. First stage or second. Free flows may cause a 1st stage to freeze up in 50 degree water.
The second stage may turn into a block of ice if they start to free flow and the air can't be shut down. Plastic barrel seconds will freeze up quicker than metal ones because metal is a better conductor of heat.
I don't like packages. I 'd rather buy the individual components to meet my needs.
Out of your choices, if I had to get a package, I'd pick the Dive Rite.
Next would be the D6 with XT2 seconds.
I would not consider the XTRA 1st because it's not sealed and I'm not a fan of unsealed piston regs for less than clear fresh water.
I'm also not crazy about the cover on the XTRA 2nd stage. Too many components.
All that said, if were buying a new reg set for backmount it would be the HOG D1s in DIN with Classic Seconds. I serviced hundreds of those over the 12 years I was doing it.
Sidemount? HOG D3 or Deep Six Signature 1sts with the same HOG Classic 2nds.