My two cents...
First of all, for cold water, you need a good diving suit. This is a truly personal item, I would not recommend to ever rent it. You need to choose between a hemi-sealed neoprene-foam suit, or a truly-sealed ("dry") suit.
The second needs to be inflated with air and this is something you have to learn (and possibly be certified for).
I did make some under-the-ice diving when young, but I always used an hemi-sealed neoprene-foam suit, I always avoided the complexity and loss of mobility (and water penetration) caused by a dry suit. Of course it also depends on depth and diving time, my under-the-ice dives were all quite short (15-20 minutes). For professional divers staying hours underwater a dry suit with proper thermally-insulating undersuit is a must!
Regarding regulators, my opinion is that in cold water nothing surpasses vintage Scubapro regulators, with an all-metal second stage, such as 109 and 156 models (I have a total of 6 of them, and they can be serviced with modern parts, and converted to fully-balanced, keeping them at the state of the art). Plastic regulators are more easy to freeze...
At first stage I have 4 Scubapro MK5 and one MK15. All of them are quipped with what was called, at the time, the "antifreeze" mod, consisting in a flooded chamber with thin holes and saturated with thermally insulating grease. Never had problems, even under 1m of ice...
The trick, indeed is NOT to use an Octopus (a single first stage with two second stages). In cold waters (but, I think, everywhere) it is much more reliable to mount two separate first stages on the air bottle, each feeding its own second stage.
Regarding BCD, I also recommend a rear-inflation system, not a bulky full-chest BCD. However, I find that a metal backplate, with fixed harnesses and a wing, is also a very bulky and heavy setup: again, it is fine for professional divers, but for an occasional recreational diver I think it is more appropriate a light rear BCD, such as the Cressi Scorpion, or, even better, the ultralight and cheap Scubapro Litehawk:
https://ww2.scubapro.com/en-GB/SWE/bcs/products/litehawk.aspx
Due to the limited buoyancy of these devices, you must be careful in choosing the proper amount of weights, but the end result will be a very streamlined asset, with very good mobility and less friction, allowing you to swim faster and with less effort: those are important safety features, I never recommend to get overloaded with bulky equipment which impedes to move easily and with small friction in the water.
Finally the Cressi Leonardo computer is just fine. I have two of them (me and my wife) and they are simple reliable, and very cheap (99 eur on Amazon on Prime Friday)... Again, pro divers will not use it, favoring more expensive and complex units. But I favor simplicity and ease of use, and for these the Leonardo is unbeatable, as you have to do nothing with its controls while diving, just have a look at the display, as it does everything automatically and always shows you everything you need to know. And it manages also Nitrox, not just air...
First of all, for cold water, you need a good diving suit. This is a truly personal item, I would not recommend to ever rent it. You need to choose between a hemi-sealed neoprene-foam suit, or a truly-sealed ("dry") suit.
The second needs to be inflated with air and this is something you have to learn (and possibly be certified for).
I did make some under-the-ice diving when young, but I always used an hemi-sealed neoprene-foam suit, I always avoided the complexity and loss of mobility (and water penetration) caused by a dry suit. Of course it also depends on depth and diving time, my under-the-ice dives were all quite short (15-20 minutes). For professional divers staying hours underwater a dry suit with proper thermally-insulating undersuit is a must!
Regarding regulators, my opinion is that in cold water nothing surpasses vintage Scubapro regulators, with an all-metal second stage, such as 109 and 156 models (I have a total of 6 of them, and they can be serviced with modern parts, and converted to fully-balanced, keeping them at the state of the art). Plastic regulators are more easy to freeze...
At first stage I have 4 Scubapro MK5 and one MK15. All of them are quipped with what was called, at the time, the "antifreeze" mod, consisting in a flooded chamber with thin holes and saturated with thermally insulating grease. Never had problems, even under 1m of ice...
The trick, indeed is NOT to use an Octopus (a single first stage with two second stages). In cold waters (but, I think, everywhere) it is much more reliable to mount two separate first stages on the air bottle, each feeding its own second stage.
Regarding BCD, I also recommend a rear-inflation system, not a bulky full-chest BCD. However, I find that a metal backplate, with fixed harnesses and a wing, is also a very bulky and heavy setup: again, it is fine for professional divers, but for an occasional recreational diver I think it is more appropriate a light rear BCD, such as the Cressi Scorpion, or, even better, the ultralight and cheap Scubapro Litehawk:
https://ww2.scubapro.com/en-GB/SWE/bcs/products/litehawk.aspx
Due to the limited buoyancy of these devices, you must be careful in choosing the proper amount of weights, but the end result will be a very streamlined asset, with very good mobility and less friction, allowing you to swim faster and with less effort: those are important safety features, I never recommend to get overloaded with bulky equipment which impedes to move easily and with small friction in the water.
Finally the Cressi Leonardo computer is just fine. I have two of them (me and my wife) and they are simple reliable, and very cheap (99 eur on Amazon on Prime Friday)... Again, pro divers will not use it, favoring more expensive and complex units. But I favor simplicity and ease of use, and for these the Leonardo is unbeatable, as you have to do nothing with its controls while diving, just have a look at the display, as it does everything automatically and always shows you everything you need to know. And it manages also Nitrox, not just air...