My dogs play and swim in icy water all the time - in the never-ending spring thaw that leaves huge puddles and ponds and swollen seasonal streams of snow melt, and in just openinig-up rivers and lakes with huge ice chunks still floating around. When they are running around and having fun, they are fine. Doesn't faze them a bit. I'm careful to not let them on the ice when I think the ice may be starting to break. Other than that, Everything is so wet, with inches of standing water on top of the ground since the snow is melting, but the ground hasn't thawed enough to take the melted water in, it would be impossible to keep them dry and clean.
They have never shown any signs of cold, like shivering. The only time I've seen either of them shivering is if they went swimming, retrieving sticks out of the water for an hour or so, and that is usually in the summer time.
In the spring, with the temps often hovering around 'just' freezing, or a few degrees below freezing, as they break through the snow crust or break the ice on melt water puddles as they run and play, they get soaked, then the water freezes in droplets on their fur - still does not bother them at all.
Then they come in and shake - What a mess!!!! I sometime just walk them around before going in the house or the car hoping they will shake that muddy, frozen water OFF first.
If I stop at a park with the dogs to give them a bit of a break and they end up in the water, I'll skip the errands I was planning on doing and take them home - I always have towels in the car to dry them off a bit, and have clean towels and blankets for them. If I know I won't be able to change my plans, I keep them away from areas where they are going to get wet.
So if you are able to get her home and dry, let Kira in the water if she wants to - won't do her any harm.