Your horse seems to understand the icy conditions and is working with it and with caution which is good and I think it is good to put them out every day, they will be aware of the conditions and not do something stupid.
A mare that I did not own but had the handling, training and showing for the first 9 yrs of her life, I would put my horses out in any weather and they knew the conditions and were smart about it.
Some time after she left my care, at the new place, there was bad weather and the horses were kept in for a few days and when they were turned out, they got running around the field and she hit a snowy patch that had ice underneath and she did the splits and broke her pelvis. She had to be put down.
I can't help but feel that if the horses were out every day this would not have happened. They would be aware of the danger areas and avoid them.