Don't worry about making new tabs or grooves. Just cut the offending tabs off. For the planks on the floor, use a sharp chisel. For the new boards, cut them on a chop saw. You want the two mating faces to be as perfectly square as possible, otherwise you will end up with a gap or one board riding up over the top of the other.
In places where you still have underlayment, a belt sander with a rough grit will take care of that in seconds. Make sure you have a shop vac hooked up to the sander!
Also, try not to have two planks next to each other where you have cut off the side and the end tab. This could lead to buckling. Provided you plan ahead on your installation pattern, this should be achievable.
Your best option is sheet vinyl. Next to that would be tile or concrete.
Most other flooring has seams which will eventually leak. Yes, you can place vinyl tiles, or even laminate flooring, if you appropriately glue/seal all the seams. Eventually the seams will leak, and in the case of laminate surface scratches must be sealed immediately to avoid damage to the laminate below the waterproof surface.
A single sheet, if possible, will provide continuous leak protection across the entire floor surface. If it's too wide for a single sheet, then a single seam is easier to keep sealed than the multiple seams found in other flooring choices.
Tile and concrete are both good options as well. Regular maintenance and upkeep will keep them in good waterproof operation for the life of the house, while vinyl will need to be replaced every decade or two.
Even though it's designed to be an unheated space, you should consider adding a vapor barrier and insulation to the flooring area. This will reduce the likelihood of later rotting or water condensation.
Keep in mind that outdoor carpet requires a sealed or well-draining surface. Your current plywood would have to be treated and sealed for the outdoor carpeting to be useful. The carpeting alone won't prevent damage to the subfloor - it will only avoid damage itself when exposed to water.
In your situation you need to protect both the flooring and the subfloor.
Regarding the cold temperatures, newer vinyl floors are much more flexible and resilient even in the fact of extreme cold weather. You'll need to specify that both the flooring and the adhesive be tolerant to freeze-thaw cycles.
Be certain that your subfloor is substantial and secure. Cracking occurs where stresses increase significantly on one area of the floor. As long as the vinyl is well-adhered to the subfloor, and the subfloor is relatively stable, then the stresses from expansion and contraction will be spread evenly across the entire surface. While these forces are large, they won't overcome the strength of the vinyl. If the subfloor develops a large gap, then the stresses in the vinyl would be greater around that gap and that's where a tear might start.
So your flooring really starts with a good, stable, strong subfloor. What you put on top, then, will be fine as long as it can deal with the water exposure.
Best Answer
It seems to depend on the range of flooring that you choose. I found a video on YouTube showing it without the tongues, and I also found a seller with some photographs showing the tongues on the edges of a piece.
This review backs up that assessment: