Well I consider my sliders "hibernating" or maybe
"brumating" is the better word.
They stay down and dormant for weeks at a time if it
is cool or cold, but they do sometimes pop up and bask
if the temps get above 70 for very long.
I think I've read that they might do this in the wild
also, depending on the climate.
If you were to put them out, I would put some type of
water heater in whatever your "pond" is so the water
doesn't completely freeze over, or freeze solid.
And I at least would let some leaves, etc., accumulate in the
bottom so they have the feeling of something to hide in.
I don't know about mud, other than it couldn't hurt. I don't
in mine because it is really just a wading pool and I don't know how that would effect keeping it clean. As it is, during the winter, I drain most of the water out and replace it every few weeks, although that is somewhat dependant on the weather. I don't bother if it is really cold. But if the weather is warm and its been awhile, I'll change the water. I change the water once a week in the spring, summer, early fall. I want to get some sort of pond filter for it and if I did have a larger pond, one that I had built in, I would definately have a filter on that.
You might check out the slider forum and see what they say about it. I had been afraid to put them out, but as they got
larger and the water changing really got to be a pain, I saw where a local naturalist, who had a "wildlife" park where you could come see his animals, left his sliders out in a man-made
cement pond that he made and it was shallower than my wading pool. I don't know if he used a heater (he died recently and the park closed) but I decided I would feel "safer" trying hibernating them if I could use a livestock water heater and keep the water from freezing.
Let me know if you have any other questions!